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

0,3

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.

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}]

Prog

(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
(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 */

Crossrefs

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

Sequence in context: A339023 A169908 A004159 * A092554 A155787 A338304

Adjacent sequences: A380582 A380583 A380584 * A380586 A380587 A380588

Keyword

nonn,base,look

Author

Giorgos Kalogeropoulos, Mar 27 2025

Status

approved