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

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

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