A253912 Fourth powers whose reversal is a prime.

16, 38416, 130321, 160000, 923521, 1500625, 13845841, 14776336, 16777216, 38950081, 163047361, 181063936, 312900721, 322417936, 384160000, 937890625, 1303210000, 1600000000, 3722098081, 7992538801, 9235210000, 13841287201, 15006250000, 16610312161, 17748900625, 31414372081, 37141383841

Offset

1,1

Comments

Intersection of A000583 and A095179.

As the last digits of primes are not even or 5 (except for primes 2 and 5), the terms do not start with an even number or 5. If m is an integer such that the reversal of m^4 is prime and sqrt4(n) is the fourth root of n then m is not of the form [sqrt4(2 * 10^k), sqrt4(3 * 10^k)] or [sqrt4(4 * 10^k), sqrt4(7 * 10^k)] for nonnegative k etc. - David A. Corneth, Jun 02 2016

All terms == 1 mod 3. - Robert Israel, Jun 03 2016

Links

Chai Wah Wu, Table of n, a(n) for n = 1..25659

Example

Example: a(1) = 16 is a fourth power because 16 = 2^4 and the reverse of 16 is 61 which is a prime number.

Mathematica

Select[Range[440]^4, PrimeQ[FromDigits@ Reverse@ IntegerDigits@ #] &] (* Michael De Vlieger, Jan 19 2015 *)

Prog

(Python)
from sympy import isprime
A253912_list = [n for n in (i**4 for i in range(10**6)) if isprime(int(str(n)[::-1]))] # Chai Wah Wu, Jun 02 2016

Crossrefs

Cf. A000583 (fourth power), A095179 (reversal of n is prime).

Cf. A058996 (primes whose reversal is a fourth power).

Sequence in context: A221244 A280656 A265662 * A017548 A265588 A185141

Adjacent sequences: A253909 A253910 A253911 * A253913 A253914 A253915

Keyword

nonn,base

Author

Rabii Younès, Jan 18 2015

Status

approved