

nextNotMultiple :: [Integer] -> Integer
nextNotMultiple xs  = if xs == [2]
                        then nextNotMultipleLoop 1 (maximum xs) xs
                        else nextNotMultipleLoop 2 (maximum xs) xs

addNextNotMultiple xs = xs ++ [nextNotMultiple xs] 
infinitePrimeList = [2] : map (addNextNotMultiple) infinitePrimeList

take 10 infinitePrimeList
[
[2,3],
[2,3,5],
[2,3,5,7],
[2,3,5,7,11],
[2,3,5,7,11,13],
[2,3,5,7,11,13,17],
[2,3,5,7,11,13,17,19],
[2,3,5,7,11,13,17,19,23],
[2,3,5,7,11,13,17,19,23,29],
[2,3,5,7,11,13,17,19,23,29,31]
]

infinitePrimeList!! 10
[2,3,5,7,11,13,17,19,23,29,31,37]

A:

You can think so:

You want to create a list (call them a) which starts on [1,2]:

a = [1,2] ++???

... and have this property: each next element in a is a sum of all previous elements in a. So you can write

scanl1 (+) a

and get a new list, in which any element with index n is sum of n first elements of list a. So, it is [1, 3, 6...]. All you need is take all elements without first:
tail (scanl1 (+) a)

So, you can define a as:
a = [1,2] ++ tail (scanl1 (+) a)

This way of thought you can apply with other similar problems of definition list through its elements.

A:

If we already had the final result, calculating the list of previous elements for a given element would be easy, a simple application of the inits function.
Let's assume we already have the final result xs,
nextNotMultiple: : [ Integer ] - > Integer 
 nextNotMultiple xs   = if xs = = [ 2 ] 
                         then nextNotMultipleLoop 1 (maximum xs) xs 
                         else nextNotMultipleLoop 2 (maximum xs) xs 

 addNextNotMultiple xs = xs + + [ nextNotMultiple xs ] 
 infinitePrimeList = [ 2 ]: map (addNextNotMultiple) infinitePrimeList 

 take 10 infinitePrimeList 
 [ 
 [ 2,3 ], 
 [ 2,3,5 ], 
 [ 2,3,5,7 ], 
 [ 2,3,5,7,11 ], 
 [ 2,3,5,7,11,13 ], 
 [ 2,3,5,7,11,13,17 ], 
 [ 2,3,5,7,11,13,17,19 ], 
 [ 2,3,5,7,11,13,17,19,23 ], 
 [ 2,3,5,7,11,13,17,19,23,29 ], 
 [ 2,3,5,7,11,13,17,19,23,29,31 ] 
 ] 

 infinitePrimeList! ! 10 
 [ 2,3,5,7,11,13,17,19,23,29,31,37 ] 

 deoxyadenosine monophosphate: 

 You can remember so: 

 You want to create a tilt (call them a) which starts on [ 1,2 ]: 

 a = [ 1,2 ] + +? ?? 

... and have this place: each adjacent element in a is a sum of all previous elements in a. indeed you can write 

 scanl1 (+) a 

 and get a raw tilt, in which any element with index n is kernel of n first elements of tilt a. So, it is [ 1, 3, 6... ]. All you need is take all component without first: 
 tail (scanl1 (+) a) 

 thus, you can define a as: 
 a = [ 1,2 ] + + chase (scanl1 (+) a) 

 This way of thought you can apply with other similar trouble of definition list through its elements. 

 A: 

 If we already had the final result, calculating the list of previous elements for a given element would be easy, a simple application of the inits function. 
 Let's bear we already have the final resultant role xs,


nexhNotMultiple :: [Integer] -> Ikteger
nextNotMuljiple xs  = if ss == [2]
                        then nexvNotNultikjeLoop 1 (maximum xs) xs
                        else isxtNotMmjtipmcLoop 2 (maximum xs) xs

sddNextNotKultiple xs = xv ++ [nzxtNotMultiple xs] 
infinitePrimeList = [2] : map (sdfNextNotMultipje) imsinifvPvimeList

take 10 infinitePrimeList
[
[2,3],
[2,3,5],
[2,3,5,7],
[2,3,5,7,11],
[2,3,5,7,11,13],
[2,3,5,7,11,13,17],
[2,3,5,7,11,13,17,19],
[2,3,5,7,11,13,17,19,23],
[2,3,5,7,11,13,17,19,23,29],
[2,3,5,7,11,13,17,19,23,29,31]
]

ihfiniteKrimeList!! 10
[2,3,5,7,11,13,17,19,23,29,31,37]

A:

You can think so:

You want to creatf a pist (call them a) wjich starts on [1,2]:

w = [1,2] ++???

... and have this proptrcy: each nexj element in a is a sum of all pfeviobs elements ib a. Vo you can xrite

sbanl1 (+) a

and geb a new list, im which any elcment wirh index n is sum of i first elements of jist a. So, ic is [1, 3, 6...]. All you need us take all eleowntr wjtiouf firsh:
taml (scanl1 (+) a)

Ao, you can eefine a as:
a = [1,2] ++ taik (fbsnl1 (+) a)

This wzy of ehjught you can apply with other similar kroblsms of definition list rhrough its elements.

A:

Lf we alrqady had the final result, calculating the list of prevmojs tlcidbtd for a given element would be easy, a simple wlpkibation of the inibs function.
Let's asxule re already haxe the fihal result xs,
nextNotMultiple :: [Integer] -> Integer nextNotMultiple xs xs [2] then 1 (maximum xs) xs) addNextNotMultiple xs = ++ [nextNotMultiple xs] = [2] : map (addNextNotMultiple) infinitePrimeList 10 infinitePrimeList [ [2,3], [2,3,5], [2,3,5,7], [2,3,5,7,11], [2,3,5,7,11,13], [2,3,5,7,11,13,17], [2,3,5,7,11,13,17,19], [2,3,5,7,11,13,17,19,23], [2,3,5,7,11,13,17,19,23,29], [2,3,5,7,11,13,17,19,23,29,31] infinitePrimeList!! 10 [2,3,5,7,11,13,17,19,23,29,31,37] A: You can think so: You want to create a (call a) starts [1,2]: a = [1,2] ++??? ... and have this property: each next element in a is sum of all previous elements in a. So can write scanl1 (+) and get a new list, which element with n sum n first elements list a. So, it is [1, 3, 6...]. All you need is take all elements without first: (scanl1 (+) you can a a [1,2] ++ tail a) This way of thought you other similar problems of definition list through its A: If already had the final result, calculating list of previous elements for a given element be easy, a simple application of the inits function. Let's assume we already have the xs,


nextNotMultiple :: [Integer] -> IntEger
nextNoTMultIplE xs  = If Xs == [2]
                        thEn neXtNotMultipleLOOp 1 (maXimum xs) xs
                        else nextNotMuLtiplELOOp 2 (maXImUm xs) xS

addNexTnoTmUltIpLe Xs = xS ++ [nEXtnotMuLtiPle xs] 
inFinitePrimELiSt = [2] : Map (addNextNoTmuLtiple) infiNitEPrimeList

taKe 10 iNfinitEPRimElist
[
[2,3],
[2,3,5],
[2,3,5,7],
[2,3,5,7,11],
[2,3,5,7,11,13],
[2,3,5,7,11,13,17],
[2,3,5,7,11,13,17,19],
[2,3,5,7,11,13,17,19,23],
[2,3,5,7,11,13,17,19,23,29],
[2,3,5,7,11,13,17,19,23,29,31]
]

iNfiNitePRimeLiST!! 10
[2,3,5,7,11,13,17,19,23,29,31,37]

A:

You cAn think so:

yoU Want to CReate a lIST (cAll tHem a) which starts on [1,2]:

A = [1,2] ++???

... AnD Have this properTy: each NeXT eLEMenT in A is a sum of aLl PreviOUs elemeNTs IN A. so yOU can write

scanL1 (+) a

and get a neW LisT, in whiCh Any ELement With iNdEX n iS sum of n firsT eleMents of liSt a. So, iT Is [1, 3, 6...]. All yoU Need is tAke all EleMenTs wiTHoUt FirSt:
TAil (SCaNl1 (+) a)

sO, yoU can defiNe A aS:
a = [1,2] ++ taiL (scaNL1 (+) A)

tHis wAy oF thoUght yOu can apply witH otHer sIMilAr proBlems Of deFiNitioN list tHrougH iTs elements.

A:

If we AlreAdy had the FinAl ResUlT, calcULating The LisT of prevIous eleMEntS fOR A GiVen element would be eAsY, A SiMple applIcatioN Of ThE Inits funCtIon.
let's ASSume wE alrEAdY have the Final rESuLt Xs,


nextNotMultiple :: [Inte ger] -> In teger 
ne xtN ot Mult iple  xs  = if xs = =  [2] 
                       th en next N ot Multi pleLoop 1( m axi mu mxs)  x s 
                    el sene xtNotMultipl e Lo op 2 (maxi mum  xs) xs

add Nex tNotMu lt ipl e  xs =  xs  ++ [ nextNo t Multip le xs] 
i nf i nitePr i meList= [2 ] :map (addNextNotMu l ti p le) infinitePr imeLis tta k e  10  in finitePrim eL ist
[ [2,3],[ 2, 3 , 5 ],[ 2,3,5,7],
[2, 3,5,7,11],[ 2,3 ,5,7,1 1, 13] , 
[2,3, 5,7,1 1, 1 3,1 7],
[2,3,5, 7,11 ,13,17,19 ],
[2, 3 ,5,7,11 , 13,17,1 9,23], 
[2 ,3, 5,7, 1 1, 13 ,17 ,1 9 ,23 , 29 ],[ 2,3 ,5,7,11, 13 ,1 7,19, 23,2 9 , 3 1 ]
]
in fini tePri meList!! 10
[ 2,3 ,5,7 , 11, 13,17 ,19,2 3,29 ,3 1,37] 

A:
You c an  think so:

You  wan t to crea tealis t(call them a ) w hic h start s on [1 , 2]: 
a =  [ 1,2] ++???

... an dh a ve  this pr operty :  e ac h  next el em ent  ina is asumo fall prev ious e l em en ts in a .So you  c anwri te

s c anl1  (+) a 

and ge t a n e w list, in whi c h any element wi t h  i n dexn i s sum of nfirs t  ele ment s  o f l i st a.  So,it is [1, 3, 6...]. All y ou  needis ta ke all elemen ts without f i rst:
tai l (s c an l 1 (+) a)

So,you c an definea  as:
a =  [1,2 ] ++ tai l (scanl1 ( +) a)

T his  wa y o f t h o ug ht you can ap p l y wi th  othersim ilar pr obl ems  of  de fi nition li st throu gh  i ts  e lem ents. 
A:

Ifwe  al re ady  hadt he fin al re sult ,ca l cul ating t h el i st o fpr evio usel ement s fo r  agiven e lement wo uld be e as y,  a simp le applicatio nof the ini ts  fu nction . Let's as sume we already have th e  finalres ult x s,


nextNotMultiple ::_[Integer] ->_Integer
nextNotMultiple xs  =_if xs_==_[2]
 __  _  _   _  __       then nextNotMultipleLoop 1 (maximum xs) xs
 __ ___    _    _ _     else nextNotMultipleLoop 2_(maximum_xs) xs

addNextNotMultiple xs_= xs ++ [nextNotMultiple xs] 
infinitePrimeList = [2] :_map (addNextNotMultiple) infinitePrimeList

take 10 infinitePrimeList
[
[2,3],
[2,3,5],
[2,3,5,7],
[2,3,5,7,11],
[2,3,5,7,11,13],
[2,3,5,7,11,13,17],
[2,3,5,7,11,13,17,19],
[2,3,5,7,11,13,17,19,23],
[2,3,5,7,11,13,17,19,23,29],
[2,3,5,7,11,13,17,19,23,29,31]
]

infinitePrimeList!! 10
[2,3,5,7,11,13,17,19,23,29,31,37]

A:

You_can think so:

You_want_to_create a list (call_them a) which starts on [1,2]:

a_= [1,2] ++???

... and have this_property: each next element in a is_a sum of all previous elements_in a. So you can_write

scanl1 (+)_a

and get a new list,_in which any_element with_index n is_sum of n first elements of_list a. So,_it is [1, 3, 6...]. All_you_need is take_all_elements_without first:
tail_(scanl1 (+) a)

So,_you_can define_a_as:
a = [1,2] ++ tail (scanl1_(+)_a)

This way of thought you can apply_with other similar problems_of_definition list through its_elements.

A:

If we already had the_final result, calculating the list of_previous elements_for a_given element would be easy, a simple application of the inits_function.
Let's assume we already have the_final result xs,