A308987 In the sequence {n^2+1} (A002522), color the primes red. When the number of terms m between successive red terms sets a new record, write down m+1.

1, 2, 4, 10, 14, 16, 20, 34, 40, 46, 88, 100, 112, 130, 152, 212, 288, 330, 346, 444, 502, 526, 534, 564, 580, 614, 624, 634, 636, 640, 690

Offset

1,2

Comments

This sequence represents the highest gaps, given by number of terms (including the starting prime) in sequence A002522 between terms which are prime.

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
...so here m=3 and we get the third term, m + 1 = 10 - 6 = 4

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, A308988.

A293564 gives essentially the same information.

Sequence in context: A034233 A056718 A057283 * A107992 A139480 A227388

Adjacent sequences: A308984 A308985 A308986 * A308988 A308989 A308990

Keyword

nonn,more

Author

Trevor Cappallo, Jul 04 2019

Extensions

a(21)-a(31) from Giovanni Resta, Jul 05 2019

Status

approved