A292084 a(n) = least prime p such that 2*p + 1 equals (2*n - 1)*q where q is a prime, or 0 if no such p exists.

0, 7, 7, 17, 13, 71, 19, 37, 59, 47, 31, 149, 37, 67, 43, 263, 181, 227, 1091, 97, 61, 107, 67, 1433, 73, 127, 79, 137, 199, 383, 701, 157, 97, 167, 103, 461, 109, 487, 269, 197, 283, 2531, 127, 739, 311, 227, 139, 617, 2861, 643, 151, 257, 157, 1979, 163, 277

Offset

1,2

Comments

Conjecture: 7 <= a(n) <= 4*n^2 - 5*n + 1 for n > 1. This conjecture implies that for every odd k > 1 there exist two primes p and q < 2*k such that k = (2*p + 1)/q.

Every positive term belongs to A053176.

Links

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000

Prog

(Magma) lst:=[]; for n in [2..56] do q:=1; repeat q+:=2; p:=Truncate((2*n*q-q-1)/2); until IsPrime(p) and IsPrime(q); Append(~lst, p); end for; [0] cat lst;
(PARI) a(n) = {if (n==1, return(0)); forprime(p=3, , q = (2*p+1)/(2*n-1); if ((denominator(q) == 1) && isprime(q), return (p)); ); } \\ Michel Marcus, Sep 16 2017

Crossrefs

Cf. A053176, A292083.

Sequence in context: A152910 A198439 A100635 * A168458 A165138 A196395

Adjacent sequences: A292081 A292082 A292083 * A292085 A292086 A292087

Keyword

nonn

Author

Arkadiusz Wesolowski, Sep 08 2017

Status

approved