login
A171267
Primes p such that p^s ends with p, where s is sum of the digits of p.
3
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
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
KEYWORD
base,nonn
AUTHOR
Farideh Firoozbakht, Apr 28 2010
EXTENSIONS
Terms a(28) onward from Max Alekseyev, Aug 18 2013
STATUS
approved