A261450 Smallest k such that A011557(n)//k//rev is prime, where rev is the string of digits of A011557(n) reversed (retaining any leading zeros) and // denotes concatenation.

0, 3, 3, 3, 5, 8, 29, 5, 8, 15, 3, 21, 8, 3, 21, 3, 8, 18, 20, 92, 110, 51, 102, 6, 57, 23, 5, 114, 8, 32, 41, 6, 236, 6, 39, 60, 110, 62, 36, 17, 53, 21, 161, 41, 159, 57, 137, 42, 83, 114, 126, 80, 30, 36, 278, 107, 425, 111, 68, 68, 95, 29, 8, 53, 426, 48

Offset: 0

Author

Felix Fröhlich, Aug 23 2015

Keywords

• nonn
• base

Comments

Is a(n) = 0 for any n > 0? If such an n exists, that n is a term of A000079 (cf. Greathouse, 2010).

All terms are congruent to 0 or 2 modulo 3, since if k is congruent to 1 modulo 3, 1000...0//k//00...01 is divisible by 3 and thus not prime.

a(n) <= A100026(n-1) with equality when a(n) is a palindrome. - Michel Marcus, Sep 11 2015

Examples

			a(1) = 3, because 10001, 10101, and 10201 are composite and 10301 is prime.
a(6) = 29, because 29 is the smallest k such that 1000000//k//0000001 is prime. The decimal expansion of that prime is 1000000290000001.
		

Links

• Dana Jacobsen, Table of n, a(n) for n = 0..500
• C. R. Greathouse IV, Primes of form 10^k + 1?, Physics Forums (message from Apr 6, 2010).

Crossrefs

Cf. A000079, A011557, A100026, A100028, A100456, A100458, A100459, A258372.

Programs

Mathematica

Table[k = 0; d = IntegerDigits[10^n]; While[! PrimeQ@ FromDigits@ Join[d, IntegerDigits@ k, Reverse@ d], k++]; k, {n, 0, 65}] (* Michael De Vlieger, Aug 26 2015 *)

PARI

a(n) = x=10^n; k=0; while(!ispseudoprime(eval(Str(x, k, concat(Vecrev(Str(x)))))), k++); k

Perl

use ntheory ":all"; for my $n (0..50) { my($t,$c)=(0); $t++ while $c=1 . 0 x $n . $t . 0 x $n . 1, !is_prob_prime($c); say "$n $t"; } # Dana Jacobsen, Oct 02 2015