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

Author

Farideh Firoozbakht, Apr 28 2010

Keywords

• base
• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A004022, A171267, A171269.

Programs

Mathematica

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

Extensions

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