OFFSET
1,3
COMMENTS
Previous name: Numbers n such that Sum_{i=1..r, x(i)^2} is a perfect square, where x(i) = digits of n. r=1+floor(log_10 n).
LINKS
Christian N. K. Anderson, Table of n, a(n) for n = 1..10000
FORMULA
n*sqrt(log n) << a(n) << n*sqrt(log n). - Charles R Greathouse IV, Dec 01 2025
EXAMPLE
34 is a term: 3^2 + 4^2 = 25 = 5^2.
122 is a term: 1^2 + 2^2 + 2^2 = 9 = 3^2.
MAPLE
select(n -> issqr(convert(map(`^`, convert(n, base, 10), 2), `+`)), [$0..1000]); # Robert Israel, Dec 08 2025
MATHEMATICA
Select[Range[0, 666], IntegerQ[Sqrt[Plus @@ (IntegerDigits[#]^2)]] &] (* Ivan Neretin, Aug 03 2015 *)
PROG
(PARI) isok(n) = {my(digs = digits(n)); issquare(sum(i=1, #digs, digs[i]^2))} \\ Michel Marcus, Jun 02 2013
(PARI) is(n)=issquare(norml2(digits(n))) \\ Charles R Greathouse IV, Dec 01 2025
(Python)
from math import isqrt
def ok(n): s = sum(int(i)**2 for i in str(n)); return isqrt(s)**2 == s
print(*[k for k in range(664) if ok(k)], sep = ', ') # Ya-Ping Lu, Jul 07 2025
CROSSREFS
KEYWORD
base,easy,nonn
AUTHOR
Ctibor O. Zizka, Apr 30 2010
EXTENSIONS
Corrected and extended by Neven Juric, Jul 12 2010
Simpler definition by Michel Marcus, Jun 02 2013
STATUS
approved
