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.
s1=s2=0;lst={};Do[If[PrimeQ[n],NULL,s1+=n;If[PrimeQ[s1],s2+=s1;AppendTo[lst,s2]]],{n,2,6!}];lst
f[ n_Integer ] := Block[ {k = n + PrimePi[ n ] + 1}, While[ k - PrimePi[ k ] - 1 != n, k++ ]; k ]; s = 0; Do[ s = s + f[ n ]; If[ PrimeQ[ s ], Print[ n ] ], {n, 1, 1000} ]
With[{cn=Accumulate[Select[Range[1000],CompositeQ]]},Position[cn,?PrimeQ]]// Flatten (* _Harvey P. Dale, Feb 09 2023 *)
lista(nn) = {my(s = 0, nb = 0); forcomposite(c=1, nn, s += c; nb++; if (isprime(s), print1(nb, ", ")););} \\ Michel Marcus, May 13 2018
from sympy import isprime A053782_list, n, m, s = [], 1, 4, 4 while len(A053782_list) < 10000: if isprime(s): A053782_list.append(n) m += 1 if isprime(m): m += 1 n += 1 s += m # Chai Wah Wu, May 13 2018
a(8) = 3 because prime(8) = 19 can be written in 3 ways as a sum of distinct composites: 19 = 9 + 10 = 9 + 4 + 6 = 15 + 4.
P:= [seq(ithprime(i),i=1..100)]:
C:= {$2..P[-1]} minus convert(P,set):
G:= mul(1+x^c,c=C):
seq(coeff(G,x,P[i]),i=1..100); # Robert Israel, Apr 22 2025
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