A088783 -id:A088783 - cp's OEIS frontend

A088622 Smallest prime obtained as the concatenation of a power of n followed by a 1, or 0 if no such number exists.

11, 41, 31, 41, 251, 61, 71, 641, 811, 101, 259374246011, 0, 131, 75295361, 151, 40961

Offset: 1

Amarnath Murthy, Oct 19 2003

a(12) = 0. Subsidiary sequence: n such that 10*n^k +1 is composite for all k >0 (indices of zero entries in this sequence): see A088783.

a(17) is too large to display here. After a(17) the sequence continues: 181, 191, 4001, 211, 1368800680154120519681, 0, 241, 251, 6761, 271, 281, 7072811, 9001, 311, 0, 331, 0, 12251, 466561, 13691, 20851361, 23134411, 401

Cf. A088623, A088782, A088783.

f[n_] := Block[{k = 1}, While[ !PrimeQ[10*n^k + 1] && k != 1500, k++ ]; If[k == 1500, 0, 10*n^k + 1]]; Table[ f[n], {n, 1, 50}] (* Robert G. Wilson v, Oct 25 2003 *)

Next term is too large to include. - Ray Chandler, Oct 23 2003

Extended by Robert G. Wilson v, Oct 25 2003

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.

Original entry on oeis.org

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

Ray Chandler, Oct 23 2003

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

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

Cf. A088622, A088783.

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 *)

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

cp's OEIS Frontend

A088622 Smallest prime obtained as the concatenation of a power of n followed by a 1, or 0 if no such number exists.

Views

Author

Keywords

Comments

Crossrefs

Programs

Mathematica

Extensions