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A053782 Numbers k such that the sum of the first k composite numbers is prime. 7
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 (list; graph; refs; listen; history; text; internal format)
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} ]

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 A071852

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

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Last modified November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)