This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309676 #6 Aug 12 2019 15:42:50
%S A309676 1,1,1,2,3,5,8,13,21,33,53,86,138,222,357,573,921,1481,2381,3828,6153,
%T A309676 9890,15898,25556,41082,66039,106156,170644,274307,440945,708815,
%U A309676 1139412,1831589,2944253,4732847,7607989,12229743,19659153,31601828,50799517,81659549
%N A309676 Number of compositions (ordered partitions) of n into odd primes (including 1).
%H A309676 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A309676 G.f.: 1/(1 - x - Sum_{k>=2} x^prime(k)).
%p A309676 a:= proc(n) option remember; `if`(n=0, 1, a(n-1)+
%p A309676 add(`if`(isprime(j), a(n-j), 0), j=3..n))
%p A309676 end:
%p A309676 seq(a(n), n=0..42); # _Alois P. Heinz_, Aug 12 2019
%t A309676 nmax = 42; CoefficientList[Series[1/(1 - x - Sum[x^Prime[k], {k, 2, nmax}]), {x, 0, nmax}], x]
%t A309676 a[0] = 1; a[n_] := a[n] = Sum[Boole[PrimeOmega[k] < 2 && OddQ[k]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 42}]
%Y A309676 Cf. A002124, A006005, A008578, A023360, A080545, A280917, A298603, A298604.
%K A309676 nonn
%O A309676 0,4
%A A309676 _Ilya Gutkovskiy_, Aug 12 2019