A249800 a(n) is the smallest prime q such that n(q+1)+1 is prime, that is, the smallest prime q such that n = (p-1)/(q+1) with p prime; or a(n) = -1 if no such q exists.

3, 2, 3, 2, 5, 2, 3, 11, 3, 2, 5, 2, 3, 2, 3, 5, 5, 3, 11, 2, 5, 2, 5, 2, 3, 2, 3, 3, 7, 5, 11, 2, 5, 2, 5, 2, 3, 5, 3, 5, 17, 2, 3, 7, 3, 2, 5, 3, 3, 2, 5, 2, 13, 2, 5, 5, 3, 3, 11, 2, 5, 5, 5, 2, 7, 2, 3, 5, 3, 2, 7, 5, 3, 2, 7, 2, 5, 3, 3, 2, 5, 113, 5, 3, 11

Offset

1,1

Comments

Variation on Schinzel's Hypothesis.

Links

Paolo P. Lava, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Schinzel's Hypothesis.

Example

For n=1 the minimum primes p and q are 5 and 3: (p-1)/(q+1) = (5-1)/(3+1) = 4/4 = 1. Therefore a(1)=3.
For n=2 the minimum primes p and q are 7 and 2: (p-1)/(q+1) = (7-1)/(2+1) = 6/3 = 2. Therefore a(2)=2.

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);

Mathematica

a249800[n_Integer] := Module[{q}, q = 2; While[CompositeQ[n (q + 1) + 1], q = NextPrime[q]]; q]; a249800/@Range[120] (* Michael De Vlieger, Nov 19 2014 *)

Prog

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

Crossrefs

Cf. A060324, A062251, A064632, A249801, A249802, A249803.

Sequence in context: A084117 A116895 A134267 * A165258 A238393 A092962

Adjacent sequences: A249797 A249798 A249799 * A249801 A249802 A249803

Keyword

nonn,easy

Author

Paolo P. Lava, Nov 06 2014

Status

approved