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A358430
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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.
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0
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2704, 74, 734, 19189898, 26509715, 69713, 4521289, 2173287, 2785343, 228207824, 570319147, 5229039, 57210987
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OFFSET
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2,1
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LINKS
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Table of n, a(n) for n=2..14.
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EXAMPLE
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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.
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PROG
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(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
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CROSSREFS
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Cf. A127335.
Cf. A358156, A357813.
Sequence in context: A254513 A254506 A254813 * A270542 A250615 A193172
Adjacent sequences: A358427 A358428 A358429 * A358431 A358432 A358433
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KEYWORD
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nonn,more
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AUTHOR
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Jean-Marc Rebert, Nov 15 2022
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STATUS
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approved
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