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A171268 Primes q such that q^p ends with q, where p is the product of the digits of q. 3

%I

%S 5,11,37,61,73,199,751,3761,7993,79193,7799999,1111111111111111111,

%T 11111111111111111111111,199999999999999999999999999

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

%C All repunit primes (A004022) are in the sequence.

%C Number 2*10^k-1 is a term whenever k is an even term of A002957. - _Max Alekseyev_, Jun 08 2018

%C 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

%H Max Alekseyev, <a href="/A171268/b171268.txt">Table of n, a(n) for n = 1..22</a>

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

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

%Y Cf. A004022, A171267, A171269.

%K base,nonn

%O 1,1

%A _Farideh Firoozbakht_, Apr 28 2010

%E a(12)-a(14) from _Max Alekseyev_, Aug 18 2013

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Last modified October 17 04:02 EDT 2019. Contains 328106 sequences. (Running on oeis4.)