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 A282906 #5 Feb 16 2025 08:33:42
%S A282906 1,0,1,0,1,1,1,2,1,3,3,4,6,5,10,9,15,18,21,32,33,52,58,79,102,122,172,
%T A282906 201,277,341,438,575,707,947,1169,1530,1949,2474,3228,4046,5281,6678,
%U A282906 8594,11035,14025,18142,23015,29681,37888,48512,62319,79456,102230,130456,167418,214356,274221,351904,449700,577024,738150
%N A282906 Expansion of 1/(1 - Sum_{j>=1} x^(Sum_{i=1..j} prime(i))).
%C A282906 Number of compositions (ordered partitions) of n into partial sums of primes (A007504).
%C A282906 Conjecture: every number > 3 is the sum of at most 5 partial sums of primes.
%H A282906 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeSums.html">Prime Sums</a>
%H A282906 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A282906 G.f.: 1/(1 - Sum_{j>=1} x^(Sum_{i=1..j} prime(i))).
%e A282906 a(11) = 4 because we have [5, 2, 2, 2], [2, 5, 2, 2], [2, 2, 5, 2] and [2, 2, 2, 5].
%t A282906 nmax = 60; CoefficientList[Series[1/(1 - Sum[x^Sum[Prime[i], {i, 1, j}], {j, 1, nmax}]), {x, 0, nmax}], x]
%Y A282906 Cf. A007504, A023360, A084143, A281273, A281274.
%K A282906 nonn
%O A282906 0,8
%A A282906 _Ilya Gutkovskiy_, Feb 24 2017