A171268 -id:A171268 - cp's OEIS frontend

A171269 Intersection of A171267 and A171268.

5, 751, 79193

Offset: 1

Farideh Firoozbakht, Apr 28 2010

Primes p such that both numbers p^A007953(p) and p^A007954(p) end with p.
a(4) > prime(10^8)=2038074743.
Number 2*10^k-1 is a term as soon as k is a multiple of 10 and belongs to A002957. In particular, a(4) <= 2*10^3020 - 1. - Max Alekseyev, Jun 07 2018

Cf. A171267, A171268.

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

Original entry on oeis.org

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

Farideh Firoozbakht, Apr 28 2010

			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.

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

Cf. A171268, A153427, A153428.

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

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

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A171269 Intersection of A171267 and A171268.

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

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