A308988 a(n) = A293564(n) - 1.
1, 2, 6, 26, 40, 94, 184, 350, 496, 3390, 3536, 45370, 82734, 99064, 357164, 840904, 3880556, 27914936, 40517520, 104715206, 1126506904, 2084910530, 2442825346, 4332318176, 6716598046, 17736392220, 18205380336, 30869303806, 68506021364, 78491213264, 85620067844
Offset: 1
Keywords
Examples
n=6 --> 6^2+1 = 37, prime n=7 --> 7^2+1 = 50, composite n=8 --> 8^2+1 = 65, composite n=9 --> 9^2+1 = 82, composite n=10 --> 10^2+1 = 101, prime ...yields the third record gap number of terms, so the start index n=6 appears as the third entry in this sequence.
Programs
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Mathematica
best = c = lastBestAt = 0; For[i = 2, True, i += 2; c += 2, If[PrimeQ[i^2 + 1], If[c > best, best = c; bestAt = i - c; If[bestAt != lastBestAt, Print[{c, bestAt}]]; lastBestAt = bestAt; ]; c = 0; ] ]
Extensions
a(21)-a(31) from Giovanni Resta, Jul 05 2019
Comments