A334287 Smallest full reptend prime p such that there is a gap of exactly 2n between p and the next full reptend prime, or 0 if no such prime exists.

17, 19, 23, 491, 7, 47, 419, 577, 29, 0, 1789, 233, 461, 433, 193, 509, 823, 61, 1979, 1327, 659, 269, 11503, 1381, 887, 14251, 3167, 8297, 3469, 0, 7247, 15073, 2473, 743, 19309, 4349, 21503, 12823, 14939, 3863, 5419, 6389, 24137, 27211, 10343, 13577, 18979

Offset

1,1

Comments

Gaps of length congruent to 20 mod 40 do not exist. All full reptend primes are either 7, 11, 17, 19, 21, 23, 29, or 33 mod 40, and no difference of 20 exists between any of these numbers.

Links

Martin Raab, Table of n, a(n) for n = 1..583

Eric Weisstein's World of Mathematics, Full Reptend Prime

Example

a(9) = 29 because there is a gap of 2*9 = 18 between 29 and the next full reptend prime 47.
a(10) = 0 because no gap of 2*10 = 20 exists between full reptend primes.

Prog

(PARI) is(p) = Mod(10, p)^(p\2)==-1 && znorder(Mod(10, p))+1==p;
isok(p, n) = {if (! is(p), return (0)); if (isprime(p+n) && is(p+n), forprime(q=p+1, p+n-1, if (is(q), return (0)); ); return (1); ); }
a(n) = {n *= 2; if ((n % 40) == 20, return (0)); my (p = 2); while (! isok(p, n), p = nextprime(p+1)); p; } \\ Michel Marcus, Apr 22 2020

Crossrefs

Cf. A001913.

Sequence in context: A288613 A154881 A226684 * A249566 A205646 A281192

Adjacent sequences: A334284 A334285 A334286 * A334288 A334289 A334290

Keyword

nonn

Author

Martin Raab, Apr 21 2020

Status

approved