%I #29 Feb 16 2020 20:52:28

%S 11,12,14,16,21,23,25,32,38,41,49,52,56,58,61,65,83,85,94,101,102,104,

%T 106,110,111,113,119,120,131,133,137,140,146,160,164,166,173,179,191,

%U 197,199,201,203,205,210,223,229,230,232,250,289,292,298,302,308

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

%C 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

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

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

%Y Cf. A108662.

%K nonn,base

%O 1,1

%A _Sumit Maheshwari_, May 09 2010