A171267 -id:A171267 - 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.

A171268 Primes q such that q^p ends with q, where p is the product of the digits of q.

Original entry on oeis.org

5, 11, 37, 61, 73, 199, 751, 3761, 7993, 79193, 7799999, 1111111111111111111, 11111111111111111111111, 199999999999999999999999999

Offset: 1

Farideh Firoozbakht, Apr 28 2010

All repunit primes (A004022) are in the sequence.
Number 2*10^k-1 is a term whenever k is an even term of A002957. - Max Alekseyev, Jun 08 2018
a(15) = 38*10^152-1, a(16) = 2*10^236-1, a(17) = 2*10^248-1, a(18) = (10^317-1)/9, a(19) = 38*10^352-1, a(20) = 2*10^386-1, a(21) = 78*10^535-1, a(22) = 2*10^546-1 are too large to include here. - Max Alekseyev, Jun 26 2018

			7799999^(7*7*9*9*9*9*9) == 7799999 (mod 10^7), so 7799999 is a term.

Max Alekseyev, Table of n, a(n) for n = 1..22

Cf. A004022, A171267, A171269.

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

a(12)-a(14) from Max Alekseyev, Aug 18 2013

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A171269 Intersection of A171267 and A171268.

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A171268 Primes q such that q^p ends with q, where p is the product of the digits of q.

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