login
Primes p such that the sum of the cubes of digits of p equals the sum of digits of p^3.
0

%I #13 Aug 29 2017 03:38:44

%S 2,31,103,1321,2003,3001,3221,10303,21323,23021,30203,30313,31123,

%T 31223,31321,32003,33013,33211,100003,102241,103231,113023,122033,

%U 122321,130223,131203,132001,132103,133201,133213,200003,203311,210233,213203,220411,221303,223211

%N Primes p such that the sum of the cubes of digits of p equals the sum of digits of p^3.

%e a(2)=31 is prime: [3^3 + 1^3 = 27 + 1] = 28; [31^3 = 29791, 2+9+7+9+1] = 28.

%e a(4)=1321 is prime: [1^3 + 3^3 + 2^3 + 1^3 = 1 + 27 + 8 + 1] = 37; [31^3 = 2305199161, 2+3+0+5+1+9+9+1+6+1] = 37.

%t Select[Prime[Range[30000]], Total[IntegerDigits[#]^3] == Plus @@ IntegerDigits[#^3] &]

%o (PARI) forprime(p=1, 30000, d=digits(p); if(sum(i=1, length(d), d[i]^3) == sumdigits(p^3), print1(p", ")));

%Y Intersection of A000040 and A165551.

%Y Cf. A000578, A030078, A235398, A290972.

%K nonn,base

%O 1,1

%A _K. D. Bajpai_, Aug 17 2017