A309883 Numbers k such that A003132(k^2) = A003132(k), where A003132(n) is the sum of the squares of the digits of n.

0, 1, 10, 35, 100, 152, 350, 377, 452, 539, 709, 1000, 1299, 1398, 1439, 1519, 1520, 1569, 1591, 1679, 1965, 2599, 2838, 3332, 3500, 3598, 3770, 4520, 4586, 4754, 4854, 5390, 5501, 5835, 5857, 6388, 6595, 6735, 6861, 6951, 7090, 7349, 7887, 8395, 9795, 10000, 10056, 10159, 10389, 11055, 11091, 12990, 12999

Offset

1,3

Comments

If k is in the sequence, then so are k*10^r, r >= 1.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

377^2 = 142129, A003132(377) = 3^2 + 7^2 + 7^2 = 107, A003132(142129) = 1^2 + 4^2 + 2^2 + 1^2 + 2^2 + 9^2 = 107.

Maple

filter:= proc(n) local t;
  add(t^2, t = convert(n, base, 10)) = add(t^2, t = convert(n^2, base, 10))
end proc:
select(filter, [$0..20000]); # Robert Israel, Apr 30 2023

Mathematica

digSum[n_] := Total[IntegerDigits[n]^2]; Select[Range[0, 13000], digSum[#] == digSum[#^2] &] (* Amiram Eldar, Aug 22 2019 *)

Prog

(PARI) for(i = 0, 30000, if(norml2(digits(i^2)) == norml2(digits(i)), print1(i, ", ")))
(Python)
def A003132(n):
    s = 0
    while n > 0:
        s, n = s+(n%10)**2, n//10
    return s
n, a = 0, 0
while n < 50:
    if A003132(a) == A003132(a*a):
        n = n+1
        print(n, a)
    a = a+1 # A.H.M. Smeets, Aug 23 2019
(Magma) [0] cat [k:k in [1..13000]| &+[c^2: c in Intseq(k)] eq &+[c^2: c in Intseq(k^2)]]; // Marius A. Burtea, Aug 24 2019

Crossrefs

Cf. A003132, A058369, A070276, A174460, A176670, A178213, A307735, A309884.

Sequence in context: A331429 A272352 A358248 * A049736 A048507 A240267

Adjacent sequences: A309880 A309881 A309882 * A309884 A309885 A309886

Keyword

nonn,base

Author

Antonio Roldán, Aug 21 2019

Status

approved