A334287 - OEIS

%I #14 Jun 01 2020 15:41:41

%S 17,19,23,491,7,47,419,577,29,0,1789,233,461,433,193,509,823,61,1979,

%T 1327,659,269,11503,1381,887,14251,3167,8297,3469,0,7247,15073,2473,

%U 743,19309,4349,21503,12823,14939,3863,5419,6389,24137,27211,10343,13577,18979

%N 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.

%C 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.

%H Martin Raab, <a href="/A334287/b334287.txt">Table of n, a(n) for n = 1..583</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FullReptendPrime.html">Full Reptend Prime</a>

%e a(9) = 29 because there is a gap of 2*9 = 18 between 29 and the next full reptend prime 47.

%e a(10) = 0 because no gap of 2*10 = 20 exists between full reptend primes.

%o (PARI) is(p) = Mod(10, p)^(p\2)==-1 && znorder(Mod(10, p))+1==p;

%o 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););}

%o 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

%Y Cf. A001913.

%K nonn

%O 1,1

%A _Martin Raab_, Apr 21 2020