Generate Numpad-Friendly Numbers
JavaScript (ES6), 104 93 89 88 bytes

Returns the N-th term of the sequence, 1-indexed.

f=(i,k,n=k,N=n/5&gt;&gt;1)=&gt;(N?8530025&gt;&gt;(n%10*6191^N%10*6191)%26&amp;1:!i--)?N?f(i,k,N):k:f(i,-~k)


Demo



f=(i,k,n=k,N=n/5&gt;&gt;1)=&gt;(N?8530025&gt;&gt;(n%10*6191^N%10*6191)%26&amp;1:!i--)?N?f(i,k,N):k:f(i,-~k)

for(n = 1; n &lt;= 50; n++) {
  console.log('a(' + n + ') = ' + f(n))
}