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

1,1

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)

Links

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

Example

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

Prog

(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

Crossrefs

Cf. A114259, A114260, A114261, A199630.

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

Sequence in context: A183788 A369238 A093212 * A238151 A234243 A260053

Adjacent sequences: A114255 A114256 A114257 * A114259 A114260 A114261

Keyword

base,nonn

Author

Giovanni Resta, Nov 18 2005

Status

approved