A144709 Integers m > 1 such that there is not a pair of primes (m^2+m-k, m^2+m+k), 1 <= k < m, between successive squares m^2 and (m+1)^2.

17, 19, 46, 58, 64, 67, 85, 367

Offset

1,1

Comments

Conjecture: the intervals (n^2,(n+1)^2) that do not contain at least one such pair are sparse as n gets large.

There are no other terms up to 2*10^7. - Michel Marcus, Aug 15 2022

Links

Table of n, a(n) for n=1..8.

Eric Weisstein's World of Mathematics, Twin Primes

Example

For m = 2,3,4, we have prime pairs (5,7), (11,13), (17,23), so these m are not terms.

Prog

(PARI) isok(n) = {for (k=1, n-1, if (isprime(n^2+n+k) && isprime(n^2+n-k), return (0)); ); return (1); } \\ Michel Marcus, Aug 31 2013

Crossrefs

Sequence in context: A108024 A095081 A243437 * A132239 A075432 A232882

Adjacent sequences: A144706 A144707 A144708 * A144710 A144711 A144712

Keyword

nonn,more

Author

Daniel Tisdale, Sep 19 2008

Extensions

Name edited by Michel Marcus, Aug 15 2022

Status

approved