A393560 a(n) is the smallest prime p for which ((n+1)*p + 1)/n is also prime.

2, 3, 2, 23, 19, 11, 41, 47, 17, 179, 43, 167, 233, 83, 29, 479, 67, 107, 227, 79, 41, 131, 229, 191, 449, 103, 701, 167, 173, 59, 2789, 127, 263, 1019, 349, 71, 887, 227, 233, 479, 163, 251, 257, 263, 359, 1931, 1409, 863, 587, 499, 101, 311, 953, 107, 2309, 223, 797, 347, 353, 479, 3659

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

Maple

f:= proc(n) local p0, d, p;
   if n::even then p0:= n-1; d:= n
   else p0:= 2*n-1; d:= 2*n
   fi;
   for p from p0 by d do
     if isprime(p) and isprime(((n+1)*p+1)/n) then return p fi
   od
end proc: f(1):= 2: f(3):= 2:
map(f, [$1..100]); # Robert Israel, Mar 23 2026

Mathematica

a[n_] := Module[{p = 2}, While[! PrimeQ[((n + 1)*p + 1)/n], p = NextPrime[p]]; p]; Array[a, 60] (* Amiram Eldar, Mar 23 2026 *)

Crossrefs

Cf. A005384, A158709, A158721, A394311.

Cf. A038700 (((n+1)*p + 1)/n is an integer).

Sequence in context: A350622 A019228 A361531 * A332734 A178134 A369190

Adjacent sequences: A393557 A393558 A393559 * A393561 A393562 A393563

Keyword

nonn

Author

Juri-Stepan Gerasimov, Mar 22 2026

Status

approved