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A114258 Numbers k such that k^2 contains exactly 2 copies of each digit of k. 18
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A183788 A369238 A093212 * A238151 A234243 A260053
KEYWORD
base,nonn
AUTHOR
Giovanni Resta, Nov 18 2005
STATUS
approved

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Last modified April 23 07:42 EDT 2024. Contains 371905 sequences. (Running on oeis4.)