A394311 a(n) is the smallest prime p for which ((n+1)*p - 1)/n is also prime.

2, 5, 13, 193, 11, 37, 211, 17, 37, 61, 67, 73, 313, 29, 181, 97, 103, 181, 229, 41, 337, 661, 967, 97, 151, 157, 109, 337, 59, 661, 1117, 193, 397, 409, 71, 577, 223, 1217, 859, 1201, 739, 421, 1291, 617, 271, 277, 659, 193, 4999, 101, 307, 3121, 107, 1297, 331, 449, 229, 10093, 1181, 1801, 367, 373

Offset

1,1

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(1) = 2 because prime 2 and ((1 + 1)*2 - 1)/1 = 3 is also prime;
a(2) = 5 because prime 5 and ((2 + 1)*5 - 1)/2 = 7 is also prime;
a(3) = 13 because prime 13 and ((3 + 1)*13 - 1)/3 = 17 is also prime.

Maple

f:= proc(n) local p;
     for p from 1 by ilcm(n, 2) do
       if isprime(p) and isprime(((n+1)*p-1)/n) then return p fi
     od
end proc:
f(1):= 2:
map(f, [$1..100]); # Robert Israel, Mar 16 2026

Mathematica

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

Prog

(PARI) isok(p, n) = my(k=((n+1)*p - 1)/n); (denominator(k)==1) && ispseudoprime(k);
a(n) = my(p=2); while (!isok(p, n), p = nextprime(p+1)); p; \\ Michel Marcus, Mar 16 2026

Crossrefs

Cf. A005382, A158708, A158720.

Sequence in context: A275698 A186450 A065797 * A196273 A128772 A272106

Adjacent sequences: A394308 A394309 A394310 * A394312 A394313 A394314

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 15 2026

Status

approved