A394311 - OEIS

%I #15 Mar 22 2026 15:56:59

%S 2,5,13,193,11,37,211,17,37,61,67,73,313,29,181,97,103,181,229,41,337,

%T 661,967,97,151,157,109,337,59,661,1117,193,397,409,71,577,223,1217,

%U 859,1201,739,421,1291,617,271,277,659,193,4999,101,307,3121,107,1297,331,449,229,10093,1181,1801,367,373

%N a(n) is the smallest prime p for which ((n+1)*p - 1)/n is also prime.

%H Robert Israel, <a href="/A394311/b394311.txt">Table of n, a(n) for n = 1..10000</a>

%e a(1) = 2 because prime 2 and ((1 + 1)*2 - 1)/1 = 3 is also prime;

%e a(2) = 5 because prime 5 and ((2 + 1)*5 - 1)/2 = 7 is also prime;

%e a(3) = 13 because prime 13 and ((3 + 1)*13 - 1)/3 = 17 is also prime.

%p f:= proc(n) local p;

%p      for p from 1 by ilcm(n,2) do

%p        if isprime(p) and isprime(((n+1)*p-1)/n) then return p fi

%p      od

%p end proc:

%p f(1):= 2:

%p map(f, [$1..100]); # _Robert Israel_, Mar 16 2026

%t a[n_] := Module[{p = 2}, While[! PrimeQ[((n+1)*p - 1)/n], p = NextPrime[p]]; p]; Array[a, 62] (* _Amiram Eldar_, Mar 15 2026 *)

%o (PARI) isok(p, n) = my(k=((n+1)*p - 1)/n); (denominator(k)==1) && ispseudoprime(k);

%o a(n) = my(p=2); while (!isok(p,n), p = nextprime(p+1)); p; \\ _Michel Marcus_, Mar 16 2026

%Y Cf. A005382, A158708, A158720.

%K nonn

%O 1,1

%A _Juri-Stepan Gerasimov_, Mar 15 2026