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

1,1

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

Links

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

Example

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

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 *)

Crossrefs

Cf. A030430, A069568.

Sequence in context: A280072 A157691 A196944 * A160693 A167442 A249974

Adjacent sequences: A112383 A112384 A112385 * A112387 A112388 A112389

Keyword

nonn,base

Author

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

Extensions

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

Name edited by Emmanuel Vantieghem, Oct 27 2022

Status

approved