A112386 Smallest prime obtained by appending one or more 1's to n, -1 if no such prime exists.

11, 211, 31, 41, 511111, 61, 71, 811, 911, 101, 1111111111111111111, 121111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111, 131, 14111111111, 151, 16111, 1711111111, 181, 191, 2011, 211, 22111, 2311, 241

Offset: 1

Author

Michel Dauchez (mdzdm(AT)yahoo.fr), Dec 04 2005

Keywords

• nonn
• base

Comments

a(37) = -1 since there is a covering of the set {371, 3711, 37111, ...} by the prime moduli 3, 7, 13, 37. Hence, there are infinitely many values -1 in the sequence (at 371, 3711, 37111, ...). - Emmanuel Vantieghem, Oct 27 2022

a(38) = -1 because 38 followed by m >= 1 1's is divisible by 3 or 37 or by (7*10^k-1)/3 if m = 3k. - Toshitaka Suzuki, Nov 07 2023

Examples

			a(5) = 511111 because 51, 511, 5111 and 51111 are not primes.
		

Links

• Toshitaka Suzuki, Table of n, a(n) for n = 1..55

Crossrefs

Cf. A030430, A069568.

Programs

Mathematica

f[n_] := Block[{k = 1, e = Floor[Log[10, n] + 1]}, While[ !PrimeQ[n*10^k + (10^k - 1)/9], k++ ]; n*10^k + (10^k - 1)/9]; Array[f, 24] (* Robert G. Wilson v, Dec 05 2005 *)
Table[SelectFirst[Table[FromDigits[PadRight[IntegerDigits[k],n,1]],{n,IntegerLength[k]+1,250}],PrimeQ],{k,25}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 30 2017 *)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Dec 05 2005

Name edited by Emmanuel Vantieghem, Oct 27 2022