cp's OEIS Frontend

A053782 Numbers k such that the sum of the first k composite numbers is prime.

%I A053782 #16 Feb 09 2023 16:50:18
%S A053782 5,14,17,20,35,36,37,43,47,48,53,54,63,64,68,73,74,75,86,101,106,127,
%T A053782 142,149,154,159,208,209,214,221,231,234,250,254,258,259,272,283,302,
%U A053782 304,329,332,346,352,374,398,417,424,439,440,445,458,471,550,551,556
%N A053782 Numbers k such that the sum of the first k composite numbers is prime.
%H A053782 Chai Wah Wu, <a href="/A053782/b053782.txt">Table of n, a(n) for n = 1..10000</a>
%t A053782 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} ]
%t A053782 With[{cn=Accumulate[Select[Range[1000],CompositeQ]]},Position[cn,_?PrimeQ]]// Flatten (* _Harvey P. Dale_, Feb 09 2023 *)
%o A053782 (Python)
%o A053782 from sympy import isprime
%o A053782 A053782_list, n, m, s = [], 1, 4, 4
%o A053782 while len(A053782_list) < 10000:
%o A053782     if isprime(s):
%o A053782         A053782_list.append(n)
%o A053782     m += 1
%o A053782     if isprime(m):
%o A053782         m += 1
%o A053782     n += 1
%o A053782     s += m # _Chai Wah Wu_, May 13 2018
%o A053782 (PARI) lista(nn) = {my(s = 0, nb = 0); forcomposite(c=1, nn, s += c; nb++; if (isprime(s), print1(nb, ", ")););} \\ _Michel Marcus_, May 13 2018
%Y A053782 Cf. A002808, A000040, A053872, A013919.
%K A053782 nonn
%O A053782 1,1
%A A053782 _G. L. Honaker, Jr._, Mar 30 2000
%E A053782 More terms from _Robert G. Wilson v_, Mar 22 2001