A108303 Numbers n such that concatenating n and the sum of the digits of n raised to their own power (A045503) produces a prime.

1, 34, 41, 43, 52, 60, 67, 85, 101, 110, 113, 122, 126, 128, 146, 148, 150, 155, 168, 175, 184, 186, 191, 202, 208, 212, 234, 241, 252, 267, 287, 300, 355, 397, 404, 423, 432, 445, 469, 511, 602, 606, 620, 627, 634, 641, 656, 680, 685, 750, 762, 793, 806, 919

Offset: 1

Author

Jason Earls, Jun 29 2005

Keywords

• base
• easy
• nonn

Comments

2^2560 produces a 782 digit prime (certified).

For purposes of this sequence, zero raised to the zero power = 1. - Harvey P. Dale, Feb 16 2020

Examples

			a(5)=52 because 5^5 + 2^2 = 3129 and 523129 is prime.
		

Crossrefs

Cf. A045503.

Programs

Mathematica

cnsdQ[n_]:=Module[{idn=IntegerDigits[n]/.(0->1),c},c=Total[idn^idn];PrimeQ[n*10^IntegerLength[c]+c]]; Select[Range[1000],cnsdQ] (* Harvey P. Dale, Feb 16 2020 *)