A249802 a(n) is the smallest prime q such that n(q-1)-1 is prime, that is, the smallest prime q so that n = (p+1)/(q-1) with p prime; or a(n) = -1 if no such q exists.

5, 3, 2, 2, 5, 2, 3, 2, 3, 3, 5, 2, 19, 2, 3, 3, 5, 2, 3, 2, 3, 3, 7, 2, 7, 5, 3, 7, 7, 2, 3, 2, 5, 3, 5, 3, 3, 2, 7, 3, 5, 2, 7, 2, 3, 19, 7, 2, 3, 5, 3, 3, 5, 2, 3, 5, 3, 7, 7, 2, 19, 2, 5, 3, 7, 3, 7, 2, 3, 3, 5, 2, 67, 2, 3, 3, 5, 5, 3, 2, 11, 3, 5, 2, 7, 11

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)=5.
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. Etc.
		

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, A249803.

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(ithprime(k)); break; fi;
od; od; end: P(10^5);

PARI

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