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

1,1

Links

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

Example

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.

Mathematica

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

Crossrefs

Cf. A171268, A153427, A153428.

Sequence in context: A142980 A062191 A367240 * A258314 A225030 A188143

Adjacent sequences: A171264 A171265 A171266 * A171268 A171269 A171270

Keyword

base,nonn

Author

Farideh Firoozbakht, Apr 28 2010

Extensions

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

Status

approved