A223707 Conjectured least number k such that prime(n) is the largest divisor of k^3 + 1, or 0 if there is no such k.

1, 2, 0, 3, 0, 4, 0, 8, 0, 0, 6, 11, 122, 7, 0, 582, 0, 14, 30, 212, 9, 24, 82, 88, 36, 1817, 47, 0, 46, 677, 20, 654, 136, 43, 2383, 33, 13, 59, 166, 1037, 210682, 49, 381, 85, 23245, 93, 15, 40, 18613, 95, 5591, 1433, 16, 0, 1798, 788, 26361, 29, 117, 842

Offset: 1

Author

T. D. Noe, Apr 03 2013

Keywords

• nonn

Comments

We allowed k to vary up to 10^7.

Crossrefs

Cf. A223701-A223706 (related sequences).

Programs

Mathematica

nn = 60; t = Table[0, {nn}]; ps = Prime[Range[nn]]; Do[num = n^3 + 1; j = 0; lastP = 0; While[num > 0 && j < nn, j++; p = ps[[j]]; While[Mod[num, p] == 0, lastP = j; num = num/p]];If[num == 1 && t[[lastP]] == 0, t[[lastP]] = n; Print[{lastP, n}]], {n, 10^7}]; t