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Smallest prime obtained by appending one or more 1's to n, -1 if no such prime exists.
6

%I #33 Jun 20 2024 02:42:20

%S 11,211,31,41,511111,61,71,811,911,101,1111111111111111111,

%T 121111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111,

%U 131,14111111111,151,16111,1711111111,181,191,2011,211,22111,2311,241

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

%C 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

%C 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

%H Toshitaka Suzuki, <a href="/A112386/b112386.txt">Table of n, a(n) for n = 1..55</a>

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

%t 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 *)

%t 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 *)

%Y Cf. A030430, A069568.

%K nonn,base

%O 1,1

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

%E Edited, corrected and extended by _Robert G. Wilson v_, Dec 05 2005

%E Name edited by _Emmanuel Vantieghem_, Oct 27 2022