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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.

%I A088782 #31 Jun 28 2025 18:14:44
%S A088782 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,
%T A088782 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,
%U A088782 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
%N 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.
%C A088782 a(185) > 10^6, see link. - _Eric Chen_, Jul 16 2019
%H A088782 Eric Chen, <a href="/A088782/b088782.txt">Table of n, a(n) for n = 1..184</a>
%H A088782 Karsten Bonath, <a href="https://www.rieselprime.de/ziki/Proth_prime_small_bases_least_n">Proth prime small bases least n</a>
%H A088782 Eric Chen, <a href="/A088782/a088782.txt">Table of n, a(n) for n = 1..500 status</a>
%t A088782 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 *)
%o A088782 (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
%Y A088782 Cf. A088622, A088783.
%K A088782 base,nonn
%O A088782 1,2
%A A088782 _Ray Chandler_, Oct 23 2003