A114258 Numbers k such that k^2 contains exactly 2 copies of each digit of k.

72576, 406512, 415278, 494462, 603297, 725760, 3279015, 4065120, 4152780, 4651328, 4915278, 4927203, 4944620, 4972826, 4974032, 4985523, 4989323, 5002245, 5016125, 6032970, 6214358, 6415002, 6524235, 7257600, 9883667

Offset: 1

Author

Giovanni Resta, Nov 18 2005

Keywords

• base
• nonn

Comments

From Chai Wah Wu, Feb 27 2024: (Start)

If k is a term, then k == 0 (mod 9) or k == 2 (mod 9) (see A370676).

First decimal digit of each term is 3 or larger. (End)

Examples

			72576 is in the sequence since its square 5267275776 contains four 7's, two 2's, two 5's and two 6's.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000 (terms 1..645 from Seiichi Manyama)

Crossrefs

Cf. A114259, A114260, A114261, A199630.

Cf. A061656, A061657, A061658, A061659, A061660, A061661, A061662, A061663, A061664.

Programs

Python

from math import isqrt
from itertools import count, islice
def A114258_gen(): # generator of terms
    for l in count(1):
        a = isqrt(10**((l<<1)-1))
        if (a9:=a%9):
            a -= a9
        for b in range(a,10**l,9):
            for c in (0,2):
                k = b+c
                if sorted(str(k)*2)==sorted(str(k**2)):
                    yield k
A114258_list = list(islice(A114258_gen(),20)) # Chai Wah Wu, Feb 27 2024