A096469 Smallest number m such that the concatenation of n+1 numbers m^0, m^1,..., m^(n-1), m^n is a prime.

1, 3, 33, 23, 237, 93, 37, 291, 421, 7, 471, 213, 1941, 29, 43, 17, 327, 1, 523, 21, 3403, 1, 13281, 3851, 3583, 3081, 1681, 157, 34989, 5411, 2431, 1229, 4767, 1021, 8397, 603, 429, 561, 6571, 47, 8601, 347, 15027, 687, 1611, 273, 29979, 201, 5719

Offset

1,2

Comments

Conjecture: This sequence is infinite. a(n) = 1 if and only if n + 1 is in the sequence A004023, so a(1) = a(18) = a(22) = a(316) = a(1030) = a(49080) = a(86452) = 1 and there are no other n less than 86453 such that a(n) = 1. Every term of this sequence is odd and for each n, 5 doesn't divide a(n). a(50) is greater than 11111.

Links

Table of n, a(n) for n=1..49.

Example

a(2) = 3 because 3^0 = 1, 3^1 = 3, and 3^2 = 9; 139 is prime and 3 is the smallest number that gives this result.
a(3) = 33 because 33^0 = 1; 33^1 = 33; 33^2 = 1089; 33^3 = 35937; 133108935937 is a prime and 33 is the smallest number that gives this result.

Mathematica

snm[n_]:=Module[{m=1}, While[!PrimeQ[FromDigits[Flatten[ IntegerDigits/@ (m^Range[0, n])]]], m++]; m]; Array[snm, 50] (* Harvey P. Dale, Aug 10 2016 *)

Crossrefs

Cf. A004023, A213072.

Sequence in context: A367565 A222683 A134474 * A106423 A077328 A106413

Adjacent sequences: A096466 A096467 A096468 * A096470 A096471 A096472

Keyword

base,nonn

Author

Farideh Firoozbakht, Jun 23 2004

Extensions

First example corrected by Harvey P. Dale, Aug 10 2016

Status

approved