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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
5, 11, 37, 61, 73, 199, 751, 3761, 7993, 79193, 7799999, 1111111111111111111, 11111111111111111111111, 199999999999999999999999999 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

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

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Last modified June 25 09:48 EDT 2019. Contains 324347 sequences. (Running on oeis4.)