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 A308988 a(n) = A293564(n) - 1. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The value of n such that a new record number of composites appear for (n+1)^2+1, (n+2)^2+1, (n+3)^2+1, ... Corresponding record gap sizes are given in A308987. LINKS EXAMPLE 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. 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;    ] ] CROSSREFS Cf. A002496, A002522, A293564, A308987. Sequence in context: A029988 A050573 A331963 * A316469 A322116 A223094 Adjacent sequences:  A308985 A308986 A308987 * A308989 A308990 A308991 KEYWORD nonn AUTHOR Trevor Cappallo, Jul 04 2019 EXTENSIONS a(21)-a(31) from Giovanni Resta, Jul 05 2019 STATUS approved

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Last modified February 18 09:15 EST 2020. Contains 332011 sequences. (Running on oeis4.)