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

Author

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

Keywords

• nonn

Links

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

Crossrefs

Cf. A002808, A000040, A053872, A013919.

Programs

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 *)

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

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

Extensions

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