A210767 Numbers whose digit sum as well as sum of the 4th powers of the digits is a prime.

11, 12, 14, 16, 21, 23, 25, 29, 32, 34, 38, 41, 43, 47, 52, 58, 61, 67, 74, 76, 83, 85, 89, 92, 98, 101, 102, 104, 106, 110, 111, 113, 119, 120, 131, 133, 140, 146, 160, 164, 166, 179, 191, 197, 201, 203, 205, 209, 210, 223, 230, 232, 250, 269, 290, 296, 302

Offset: 1

Author

Jonathan Vos Post, May 10 2012

Keywords

• nonn
• base
• easy

Comments

This is to the exponent 4 as A182404 is to the exponent 2.

Examples

			21 is in the sequence because sum of digits 2+1= 3 is prime, and sum of the 4th powers of the digits 2^4+1^4=17 is a prime.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A055013, A182404.

Programs

Mathematica

Select[Range[350],AllTrue[{Total[IntegerDigits[#]],Total[ IntegerDigits[ #]^4]},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 01 2019 *)

PARI

dspow(n,b,k)=my(s);while(n,s+=(n%b)^k;n\=b);s
select(n->isprime(sumdigits(n))&&isprime(dspow(n,10,4)), vector(10^3, i, i)) \\ Charles R Greathouse IV, May 11 2012

Formula

{n such that A055013(n) and A007953(n) are both primes}.