

A171268


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


3



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

1,1


COMMENTS

All repunit primes (A004022) are in the sequence.
Number 2*10^k1 is a term whenever k is an even term of A002957.  Max Alekseyev, Jun 08 2018
a(15) = 38*10^1521, a(16) = 2*10^2361, a(17) = 2*10^2481, a(18) = (10^3171)/9, a(19) = 38*10^3521, a(20) = 2*10^3861, a(21) = 78*10^5351, a(22) = 2*10^5461 are too large to include here.  Max Alekseyev, Jun 26 2018


LINKS

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


EXAMPLE

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


MATHEMATICA

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


CROSSREFS

Cf. A004022, A171267, A171269.
Sequence in context: A005178 A065315 A065317 * A152563 A077466 A074626
Adjacent sequences: A171265 A171266 A171267 * A171269 A171270 A171271


KEYWORD

base,nonn


AUTHOR

Farideh Firoozbakht, Apr 28 2010


EXTENSIONS

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


STATUS

approved



