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 A052467 #37 Feb 16 2025 08:32:42
%S A052467 0,1,3,6,11,20,37,70,134,255,476,869,1564,2821,5201,9948,19793,40562,
%T A052467 84271,174952,359576,728805,1457402,2885051,5681277,11185110,22103926,
%U A052467 43939533,87864092,176447165,354929146,713198803,1428312446,2846268351
%N A052467 Binomial transform of {b(n)}, where b(n)=1 for prime n and b(n)=0 otherwise.
%C A052467 Number of compositions of n into a prime number of parts. - _Vladeta Jovovic_, Jan 31 2005
%C A052467 The number of pernicious numbers (A052294) between 2^(n-1) and 2^n. Although the graph looks almost like 2^n, the graph of a(n)/2^n has quite a bit of variation. - _T. D. Noe_, Mar 14 2009
%H A052467 T. D. Noe, <a href="/A052467/b052467.txt">Table of n, a(n) for n = 1..1000</a>
%H A052467 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialTransform.html">Binomial Transform</a>.
%F A052467 G.f.: Sum_{k>=1} (x/(1 - x))^prime(k). - _Ilya Gutkovskiy_, Dec 28 2016
%F A052467 a(n) = A121497(n+1) - A121497(n). - _Wesley Ivan Hurt_, Jan 14 2022
%t A052467 b[n_] := Boole[ PrimeQ[n]]; a[n_] := Sum[ Binomial[n, k]*b[k], {k, 0, n}]; Table[a[n], {n, 0, 34}] // Differences (* _Jean-François Alcover_, Oct 25 2012 *)
%Y A052467 Cf. A038499.
%Y A052467 Cf. A010051, A121497.
%K A052467 nonn
%O A052467 1,3
%A A052467 _Eric W. Weisstein_
%E A052467 More terms from _David Wasserman_, Feb 25 2002
%E A052467 Description corrected by _T. D. Noe_, May 17 2003