Display OEIS sequences The On-Line Encyclopedia of Integer Sequences (OEIS) is an online database of integer sequences. It contains nearly 280000 sequences of mathematical interest. 

Examples of sequences: 


positive integers (A000027)
prime numbers (A000040)
Fibonacci numbers (A000045)


Your task is to write a program or function that displays as many OEIS sequences as you can, with a source code of 100 bytes maximum. Your program should accept as input the sequence id (without the prepending A and the zeroes), and output the 20 first numbers in that sequence.

You are not allowed to fetch the data directly from the OEIS website; all sequences must be computed by your code.

Scoring

Score is the number of OEIS sequences the program can display.
Answers will have to list the IDs of the sequences recognised by their program.

Example

Here's a valid answer in Java 8:

(int a) -&gt; {
    for (int i = 0; i &lt; 20; i++) {
        System.out.println(a==27?i+1:i*i); 
    }
};


This program can display the positive integers (A000027 - input 27) and the squares (A000290 - input 290), thus its score is 2.

Note

Please avoid scraping the whole OEIS website :-) you can download the sequence names (about 3 megs) or sequence values (about 9 megs). Note that this download is covered by the OEIS End-User License Agreement.
Python 2, 875 sequences



print', '.join('%020d'%(10**20/(input()-21004)))


Works for 875 of the sequences 21016 (decimal digits of 1/12) through 21999 (decimal digits of 1/995). 

I found this chunk with the sophisticated search algorithm of haphazardly typing in sequence id's by hand. Some of the sequences in the range are not of this format and appear elsewhere (thanks to Mitchell Spector for pointing this out). For example, 21021 is not the expansion of 1/17. 

Even with the interruptions, the sequences for 1/n appear as id n+21004. The remainder is not shifted, but the missing sequences appear elsewhere. For example, 1/17 appears as 7450. 

I counted the ones that match using a downloaded copy of the sequence names.

A different block gives 848 sequences from 16742 to 17664.

n=input()-16729
for i in range(20):k=n/12;a=int((8*k+1)**.5/2+.5);print(a*i+k-a*(a-1)/2)**(n%12+1)


These all have form n -&gt; (a*n+b)^c, where 2≤a≤12, 0≤b&lt;a, 1≤c≤12. The code extracts the coefficients via inverting triangular numbers and moduli. As before, not all sequences in the range match. If these two expressions could fit in 100 bytes, it would give 1723 sequences.

Promising chunks:


1929 matching sequences: 41006 through 42397, numerators and denominators of continued fraction convergents.
~3300 matching sequences: 147999 to 151254: counts of walks on Z^3, if you can find how the vector lists are ordered.


Here are categories for other potential chunks, via grouping the OEIS sequence names by removing all numbers (digits, minus sign, decimal point). They are sorted by number of appearances.

3010    Number of walks within N^ (the first octant of Z^) starting at (,,) and consisting of n steps taken from {(, , ), (, , ), (, , ), (, , ), (, , )}
2302    Number of reduced words of length n in Coxeter group on  generators S_i with relations (S_i)^ = (S_i S_j)^ = I
979     Primes congruent to  mod 
969     Numerators of continued fraction convergents to sqrt()
967     Denominators of continued fraction convergents to sqrt()
966     Continued fraction for sqrt()
932     Decimal expansion of /
894     Duplicate of A
659     Partial sums of A
577     Divisors of 
517     Inverse of th cyclotomic polynomial
488     Expansion of /((x)(x)(x)(x))
480     Decimal expansion of th root of 
471     Number of nX  arrays with each element x equal to the number its horizontal and vertical neighbors equal to ,,,, for x=,,,,
455     First differences of A
448     Decimal expansion of log_ ()
380     Numbers n such that string , occurs in the base  representation of n but not of n+
378     Erroneous version of A
375     Numbers n such that string , occurs in the base  representation of n but not of n
340     Numbers n with property that in base  representation the numbers of 's and 's are  and , respectively




35 sequences:

c=input()
for n in range(20):print[(c-1010)**n,(c-8582)*n][c&gt;2e3]


Works from 8585 (multiples of 3) through 8607 (multiples of 25), and 1018 (powers of 8) through 1029 (powers of 19). Conveniently, these are all in one chunk ordered by id. 

This uses only 65 of the 100 allowed bytes and isn't fully golfed yet, so I'll look for another nice chunk.