A100458 -id:A100458 - cp's OEIS frontend

A100028 Values of n for which the decimal number 10...030...01 is an n-digit prime.

3, 5, 7, 9, 23, 29, 33, 185, 267, 307, 757, 897, 1571, 2977, 3831, 4595, 6573, 9511, 11651, 15641, 68885, 69883

Offset: 1

Harvey Dubner (harvey(AT)dubner.com), Nov 20 2004

			The corresponding primes are 131, 10301, 1003001, 100030001, 10000000000300000000001, etc.

Cf. A100026, A100027, A100456, A100457, A100458, A100459.

IntegerLength/@Select[Table[FromDigits[Join[PadRight[{1},n,0],{3},PadLeft[ {1},n,0]]],{n,35000}],PrimeQ] (* Harvey P. Dale, Dec 20 2019 *)

a(n) = 2*(A171376(n+1))+1. - Chai Wah Wu, Aug 20 2015

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.

Original entry on oeis.org

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

Felix Fröhlich, Aug 23 2015

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

			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.

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).

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

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 *)

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

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

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A100028 Values of n for which the decimal number 10...030...01 is an n-digit prime.

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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.

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