A093868 Smallest prime that differs from a multiple of n by unity.

2, 3, 2, 3, 11, 5, 13, 7, 17, 11, 23, 11, 53, 13, 29, 17, 67, 17, 37, 19, 41, 23, 47, 23, 101, 53, 53, 29, 59, 29, 61, 31, 67, 67, 71, 37, 73, 37, 79, 41, 83, 41, 173, 43, 89, 47, 281, 47, 97, 101, 101, 53, 107, 53, 109, 113, 113, 59, 353, 59, 367, 61, 127, 127, 131, 67, 269

Offset: 1

Author

Amarnath Murthy, Apr 20 2004

Keywords

• nonn
• look

Comments

Numbers n such that a(n-1)=a(n+1)=n are A025584 (primes p such that p-2 is not a prime). - Rick L. Shepherd, Aug 23 2004

Links

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

Crossrefs

Cf. A093869.

Cf. A034694 (Smallest prime == 1 (mod n)), A038700 (Smallest prime == -1 (mod n)).

Programs

Maple

f:= proc(n) local j,k;
  for k from 1 do
    for j in [-1,1] do
      if isprime(k*n+j) then return k*n+j fi
  od od
end proc:
map(f, [$1..100]); # Robert Israel, Nov 07 2019

Mathematica

a[n_] := Module[{p}, For[p = 2, True, p = NextPrime[p], If[Divisible[p-1, n] || Divisible[p+1, n], Return[p]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 04 2023 *)

PARI

a(n) = forprime(p=2, , if (!((p+1) % n) || !((p-1) % n), return (p))); \\ Michel Marcus, Aug 08 2014

Formula

a(n) = min(A034694(n), A038700(n)) for all n >= 1. - Rick L. Shepherd, Aug 23 2004

Extensions

More terms from Rick L. Shepherd, Aug 23 2004