A249803 Take smallest prime q such that n(q-1)-1 is prime (A249802), that is, the smallest prime q so that n = (p+1)/(q-1) with p prime; sequence gives values of p; or -1 if A249802(n) = -1.

3, 3, 2, 3, 19, 5, 13, 7, 17, 19, 43, 11, 233, 13, 29, 31, 67, 17, 37, 19, 41, 43, 137, 23, 149, 103, 53, 167, 173, 29, 61, 31, 131, 67, 139, 71, 73, 37, 233, 79, 163, 41, 257, 43, 89, 827, 281, 47, 97, 199, 101, 103, 211, 53, 109, 223, 113, 347, 353, 59, 1097

Offset: 1

Author

Paolo P. Lava, Nov 06 2014

Keywords

• nonn
• easy

Comments

Variation on Schinzel's Hypothesis.

Examples

			For n=1 the minimum primes p and q are 3 and 5: (p+1)/(q-1) = (3+1)/(5-1) = 4/4 = 1. Therefore a(1)=3.
For n=2 the minimum primes p and q are 3 and 3: (p+1)/(q-1) = (3+1)/(3-1) = 4/2 = 2. Therefore a(2)=3.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Schinzel's Hypothesis.

Crossrefs

Cf. A060324, A062251, A064632, A249800, A249801, A249802.

Programs

Maple

with(numtheory): P:=proc(q) local k,n;
for n from 1 to q do for k from 1 to q do
if isprime(n*(ithprime(k)-1)-1) then print(n*(ithprime(k)-1)-1);
break; fi; od; od; end: P(10^5);

PARI

a(n) = my(q=2); while(! isprime(p=n*(q-1)-1), q = nextprime(q+1)); p; \\ Michel Marcus, Nov 07 2014