cp's OEIS Frontend

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.

%I A249803 #17 Feb 16 2025 08:33:24
%S A249803 3,3,2,3,19,5,13,7,17,19,43,11,233,13,29,31,67,17,37,19,41,43,137,23,
%T A249803 149,103,53,167,173,29,61,31,131,67,139,71,73,37,233,79,163,41,257,43,
%U A249803 89,827,281,47,97,199,101,103,211,53,109,223,113,347,353,59,1097
%N 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.
%C A249803 Variation on Schinzel's Hypothesis.
%H A249803 Paolo P. Lava, <a href="/A249803/b249803.txt">Table of n, a(n) for n = 1..1000</a>
%H A249803 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SchinzelsHypothesis.html">Schinzel's Hypothesis</a>.
%e A249803 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.
%e A249803 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.
%p A249803 with(numtheory): P:=proc(q) local k,n;
%p A249803 for n from 1 to q do for k from 1 to q do
%p A249803 if isprime(n*(ithprime(k)-1)-1) then print(n*(ithprime(k)-1)-1);
%p A249803 break; fi; od; od; end: P(10^5);
%o A249803 (PARI) a(n) = my(q=2); while(! isprime(p=n*(q-1)-1), q = nextprime(q+1)); p; \\ _Michel Marcus_, Nov 07 2014
%Y A249803 Cf. A060324, A062251, A064632, A249800, A249801, A249802.
%K A249803 nonn,easy
%O A249803 1,1
%A A249803 _Paolo P. Lava_, Nov 06 2014