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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 October 19 10:51 EDT 2019. Contains 328216 sequences. (Running on oeis4.)