A088782 a(n) is the smallest k>0 such that concatenation of n^k and 1 is prime, or 0 if no such number exists.

1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 10, 0, 1, 6, 1, 3, 1356, 1, 1, 2, 1, 15, 0, 1, 1, 2, 1, 1, 4, 2, 1, 0, 1, 0, 2, 3, 2, 4, 4, 1, 2, 1, 1, 6, 0, 1, 2, 2, 1, 4, 3, 1, 16, 1, 9, 0, 1, 2, 36, 1, 165, 66, 1, 1, 0, 1, 0, 6, 1, 1, 2, 12, 3, 138, 1, 1, 4, 0, 5, 4, 1, 1, 2, 5, 2, 2, 3, 1, 0, 2, 1, 24, 2, 1, 42, 7, 1, 0, 1

Offset: 1

Author

Ray Chandler, Oct 23 2003

Keywords

• base
• nonn

Comments

a(185) > 10^6, see link. - Eric Chen, Jul 16 2019

Links

• Eric Chen, Table of n, a(n) for n = 1..184
• Karsten Bonath, Proth prime small bases least n
• Eric Chen, Table of n, a(n) for n = 1..500 status

Crossrefs

Cf. A088622, A088783.

Programs

Mathematica

f[n_] := Block[{k = 1}, While[ !PrimeQ[10*n^k + 1], k++ ]; k]; f[1] = 1; Table[ f[n], {n, 1, 11}] (* Robert G. Wilson v, Oct 29 2003 *)

PARI

a(n)=if((n%11==1 || n%33==32) && n>1, 0, for(k=1, 10^6, if(ispseudoprime(10*n^k+1), return(k)))) \\ Eric Chen, Jul 16 2019