A224904 Primes p such that the decimal expansion of p^5 ends in p.

2, 3, 5, 7, 43, 193, 251, 307, 443, 499, 557, 751, 1249, 1693, 3307, 4999, 5443, 5807, 7057, 7499, 20807, 22943, 31249, 49999, 52057, 54193, 56249, 79193, 97943, 281249, 672943, 4218751, 4999999, 5422943, 8281249, 8704193, 17077057, 74218751, 407922943

Offset: 1

Author

K. D. Bajpai, Jul 25 2013

Keywords

• nonn
• base

Comments

Subsequence of A068407. - Giovanni Resta, Jul 25 2013

Examples

			193 is a prime and 193^5=267785184193 ends in 193, hence 193 is in the sequence.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A068407.

Programs

Maple

with(numtheory):with(StringTools):KD := proc() local a,b,d,e,f; a:= ithprime(n);b:= a^5;d:=length(a);e:=floor(b/(10^d))*10^d;f:=b-e;if a=f then RETURN (a) fi:end:seq(KD(),n=1..500000);

Mathematica

d[n_] := Block[{x}, Select[x /. List@ ToRules@ Reduce[x^5 == x, {x}, Modulus -> 10^n], # > 10^(n-1) && PrimeQ@# &]]; Union @@ d /@ Range@ 9 (* Giovanni Resta, Jul 25 2013 *)

PARI

is(n)=isprime(n) && Mod(n,10^#digits(n))^5==n \\ Charles R Greathouse IV, Jul 26 2013

Extensions

a(35)-a(39) from Giovanni Resta, Jul 25 2013