A248743 Smallest prime Q such that there is a prime R such that Q*(R+1)+1 or Q*(R+1)-1 or Q*(R-1)+1 or Q*(R-1)-1 is prime(n), or 0 if no such prime Q exists.

3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 3, 3, 2, 2, 2, 2, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 2, 2, 3, 2, 2, 2, 47, 3, 3, 2, 2, 2, 2, 2, 2, 2, 11, 2, 23, 17, 2, 2, 2, 2, 2, 3

Offset

1,1

Comments

The first prime prime(n) with no solution is prime(1300)=10657.

There are 43 terms 0 within the first 10000 primes.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

2=3*(2-1)-1, so a(1)=3.
3=2*(3-1)-1, so a(2)=2.
5=2*(2+1)-1=2*(3-1)+1, so a(3)=2.
7=2*(2+1)+1=2*(3+1)-1=2*(5-1)-1, so a(4)=2.

Prog

(PARI) a(p) = {if (p == 2, return (3)); forprime (q=2, p, if (!((p-1) % q) && (isprime((p-1)/q+1) || isprime((p-1)/q-1)), return (q)); if (!((p+1) % q) && (isprime((p+1)/q+1) || isprime((p+1)/q-1)), return (q)); ); } \\ to be used with a forprime loop; Michel Marcus, Oct 28 2014

Crossrefs

Sequence in context: A262626 A104435 A178815 * A085398 A252503 A270003

Adjacent sequences: A248740 A248741 A248742 * A248744 A248745 A248746

Keyword

nonn

Author

Pierre CAMI, Oct 13 2014

Status

approved