A240624 Prime numbers n such that replacing each digit d in the decimal expansion of n with d^d produces a prime. Zeros are not allowed.

11, 13, 17, 31, 53, 61, 71, 79, 151, 167, 229, 233, 251, 263, 311, 313, 331, 337, 349, 367, 389, 419, 443, 673, 751, 947, 971, 991, 1433, 1531, 1699, 1733, 1993, 2111, 2141, 2153, 2221, 2333, 2393, 2521, 2833, 2963, 3137, 3167, 3323, 3343, 3371, 3389, 3391

Offset: 1

Author

Michel Lagneau, Apr 09 2014

Keywords

• nonn
• base

Comments

Subsequence of A240623.

If zeros are counted with the convention 0^0 = 1, we find the additional primes 409, 2011, 2027, 2053, 2063, 2081, 2503, 3037, 3061, 3067, 4093, 6029, 6079, 6203, 7001, 8011, 8101, 8807, 9043, 9403, 10103, 10141, 10211, 10321, 10513, 10663, 11003, 11027, 11503, 12037,...

Examples

			263 is in the sequence because 263 becomes 44665627 which is also prime, where 44665627 is the concatenation (2^2, 6^6, 3^3) = (4, 46656, 27).
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A068492, A240623.

Programs

Mathematica

lst={};f[n_]:=Block[{a=IntegerDigits[n],b="",k=1,l},l=Length[a];While[kHarvey P. Dale, Dec 16 2014 *)