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

Author

Martin Raab, Apr 21 2020

Keywords

• nonn

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.

Examples

			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.
		

Links

• Martin Raab, Table of n, a(n) for n = 1..583
• Eric Weisstein's World of Mathematics, Full Reptend Prime

Crossrefs

Cf. A001913.

Programs

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