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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

Table of n, a(n) for n=1..31.

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.)