A380585 a(n) = floor(n^2 / 10^m) + (n^2 mod 10^m) where m is the number of decimal digits in n.

0, 1, 4, 9, 7, 7, 9, 13, 10, 9, 1, 22, 45, 70, 97, 27, 58, 91, 27, 64, 4, 45, 88, 34, 81, 31, 82, 36, 91, 49, 9, 70, 34, 99, 67, 37, 108, 82, 58, 36, 16, 97, 81, 67, 55, 45, 37, 31, 27, 25, 25, 27, 31, 37, 45, 55, 67, 81, 97, 115, 36, 58, 82, 108, 136, 67, 99

Offset: 0

Author

Giorgos Kalogeropoulos, Mar 27 2025

Keywords

• nonn
• base
• look

Comments

The positive fixed points of this sequence are the Kaprekar numbers (A053816).

The sum of two halves of the decimal expansion of n^2 after having added a leading 0 if that number of digits is odd. - Michel Marcus, Mar 28 2025

Links

• Giorgos Kalogeropoulos, Table of n, a(n) for n = 0..10000
• Seiichi Manyama, Post 191006
• Ivo Zerkov, 22222^2, seqfan post.

Crossrefs

Cf. A053816 (fixed points), A055642, A344851, A358072 (similar plot).

Programs

Maple

a:= n-> (k-> iquo(n^2, k)+(n^2 mod k))(10^length(n)):
seq(a(n), n=0..66);  # Alois P. Heinz, Mar 27 2025

Mathematica

Table[m=IntegerLength@n; Floor[n^2/10^m] + Mod[n^2,10^m], {n,0,66}]

PARI

a(n) = my(d=digits(n^2)); if (#d % 2, d = concat(0, d)); my(m=#d/2); fromdigits(Vec(d,m)) + fromdigits(vector(#d-m, i, d[m+i])); /* Michel Marcus, Mar 28 2025 */

Python

def a(n): return (nn:=n**2)//(M:=10**len(str(n))) + nn%M
print([a(n) for n in range(0, 67)]) # Michael S. Branicky, Mar 27 2025