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 A358430 Define sp(k,n) to be the sum of n^3 consecutive primes starting at prime(k). Then a(n) is the least number k such that sp(k,n) is a cube, or -1 if no such number exists. 0
 2704, 74, 734, 19189898, 26509715, 69713, 4521289, 2173287, 2785343, 228207824, 570319147, 5229039, 57210987 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 LINKS EXAMPLE a(2) = 2704 because sp(k,2) at k = 2794 is prime(2704) + prime(2705) + ... + prime(2704 + 2^3 - 1) = 24359 + 24371 + ... + 24419 = 195112 = 58^3, a cube, and no smaller k has this property. a(3) = 74 because sp(k,3) at k = 74 is prime(74) + prime(75) + ... + prime(74 + 3^3 - 1) = 373 + 379 + ... + 541 = 12167 = 23^3, a cube, and no smaller k has this property. PROG (PARI) a(n)=my(k=1, vp=primes(n^3), s=vecsum(vp)); while(!ispower(s, 3), p=nextprime(vp[#vp]+1); s+=(p-vp[1]); vp=concat(vp, p); vp=vp[^1]; k++); k CROSSREFS Cf. A127335. Cf. A358156, A357813. Sequence in context: A254513 A254506 A254813 * A270542 A250615 A193172 Adjacent sequences: A358427 A358428 A358429 * A358431 A358432 A358433 KEYWORD nonn,more AUTHOR Jean-Marc Rebert, Nov 15 2022 STATUS approved

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Last modified March 21 07:38 EDT 2023. Contains 361393 sequences. (Running on oeis4.)