A171267 Primes p such that p^s ends with p, where s is sum of the digits of p.

5, 29, 193, 557, 751, 3307, 4999, 7499, 16693, 20807, 31249, 59999, 60443, 79193, 812501, 918751, 5422943, 46295807, 55781249, 74218751, 78281249, 89218751, 89999999, 282922943, 316295807, 674218751, 1583704193, 3824218751, 3958704193, 4092077057, 6342077057, 8324218751, 31666295807, 47779577057, 64478795807, 66666295807, 75000000001

Offset: 1

Author

Farideh Firoozbakht, Apr 28 2010

Keywords

• base
• nonn

Examples

			1583704193^(1+5+8+3+7+0+4+1+9+3)=1583704193 (mod 10^10) so 1583704193 is
in the sequence.
It is interesting that each of the four numbers 751^(7+5+1), 751^(7*5*1),
751^pi(751) and 751^prime(751) ends with 751.
		

Links

• Max Alekseyev, Table of n, a(n) for n = 1..107

Crossrefs

Cf. A171268, A153427, A153428.

Programs

Mathematica

Do[n=Prime[m];a=IntegerDigits[n];If[PowerMod[n,Apply[Plus,a],10^Length[a]]
==n,Print[n]],{m,100000000}]

Extensions

Terms a(28) onward from Max Alekseyev, Aug 18 2013