A182404 Numbers whose digit sum as well as sum of the squares of the digits is a prime.

11, 12, 14, 16, 21, 23, 25, 32, 38, 41, 49, 52, 56, 58, 61, 65, 83, 85, 94, 101, 102, 104, 106, 110, 111, 113, 119, 120, 131, 133, 137, 140, 146, 160, 164, 166, 173, 179, 191, 197, 199, 201, 203, 205, 210, 223, 229, 230, 232, 250, 289, 292, 298, 302, 308

Offset

1,1

Comments

Note that the cube analog "Numbers whose digit sum as well as sum of the cubes of the digits is a prime" only occurs when A007953(n) = Digital sum (i.e., sum of digits) of n) = 2, as otherwise A055012(n) = Sum of cubes of digits of n = 2, i.e., n = 2, 11, 20, 101, 110, 1001, 1010, ... since for natural numbers A^3 + B^3 is divisible by A+B. Hence "Numbers whose digit sum as well as sum of the cubes of the digits is a prime" begins 2, 11, 101, ... . - Jonathan Vos Post, May 10 2012

Links

Table of n, a(n) for n=1..55.

Example

25 is here because 2 + 5 = 7 and 2*2 + 5*5 = 29 both are prime.

Mathematica

fQ[n_] := Module[{d = IntegerDigits[n]}, PrimeQ[Total[d]] && PrimeQ[Total[d^2]]]; Select[Range[500], fQ] (* T. D. Noe, May 09 2012 *)

Crossrefs

Cf. A108662.

Sequence in context: A140353 A108662 A210767 * A234021 A264023 A177902

Adjacent sequences: A182401 A182402 A182403 * A182405 A182406 A182407

Keyword

nonn,base

Author

Sumit Maheshwari, May 09 2010

Status

approved