login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Numbers k such that concatenating k and the sum of the digits of k raised to their own power (A045503) produces a square.
0

%I #14 Mar 05 2024 14:42:28

%S 0,211,220,235,20403,111416,1011231,3444142,10003400,22303600,

%T 31151021,53231032,121542025,126423126,202032110,243425212,302434003,

%U 311544033,324231521,334130241,375607602,406221650,561620561,662033363,1053045074

%N Numbers k such that concatenating k and the sum of the digits of k raised to their own power (A045503) produces a square.

%e 235 is a term because 2^2 + 3^3 + 5^5 = 3156 and 2353156 = 1534^2.

%o (PARI) f(n)=if(n, n=digits(n); sum(i=1, #n, n[i]^n[i]), 1); \\ A045503

%o isok(k) = issquare(fromdigits(concat(digits(k), digits(f(k))))); \\ _Michel Marcus_, Mar 05 2024

%Y Cf. A045503, A108302.

%K base,nonn

%O 1,2

%A _Jason Earls_, Jul 04 2005

%E More terms from _Ryan Propper_, Jul 07 2005