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

1,2

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

Links

Table of n, a(n) for n=1..54.

Example

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

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 *)

Crossrefs

Cf. A045503.

Sequence in context: A296096 A337695 A045044 * A062695 A107730 A320703

Adjacent sequences: A108300 A108301 A108302 * A108304 A108305 A108306

Keyword

base,easy,nonn

Author

Jason Earls, Jun 29 2005

Status

approved