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

5, 14, 17, 20, 35, 36, 37, 43, 47, 48, 53, 54, 63, 64, 68, 73, 74, 75, 86, 101, 106, 127, 142, 149, 154, 159, 208, 209, 214, 221, 231, 234, 250, 254, 258, 259, 272, 283, 302, 304, 329, 332, 346, 352, 374, 398, 417, 424, 439, 440, 445, 458, 471, 550, 551, 556

Offset

1,1

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Mathematica

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 *)

Prog

(Python)
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
(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

Crossrefs

Cf. A002808, A000040, A053872, A013919.

Sequence in context: A306772 A230058 A230091 * A296692 A102884 A356873

Adjacent sequences: A053779 A053780 A053781 * A053783 A053784 A053785

Keyword

nonn

Author

G. L. Honaker, Jr., Mar 30 2000

Extensions

More terms from Robert G. Wilson v, Mar 22 2001

Status

approved