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

1,1

Comments

Subsequence of A068407. - Giovanni Resta, Jul 25 2013

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A068407.

Sequence in context: A279954 A120804 A092066 * A028981 A223035 A096843

Adjacent sequences: A224901 A224902 A224903 * A224905 A224906 A224907

Keyword

nonn,base

Author

K. D. Bajpai, Jul 25 2013

Extensions

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

Status

approved