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

1,2

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: A050573 A337573 A331963 * A343753 A316469 A322116

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