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

%I A114258 #27 Feb 28 2024 01:37:25
%S A114258 72576,406512,415278,494462,603297,725760,3279015,4065120,4152780,
%T A114258 4651328,4915278,4927203,4944620,4972826,4974032,4985523,4989323,
%U A114258 5002245,5016125,6032970,6214358,6415002,6524235,7257600,9883667
%N A114258 Numbers k such that k^2 contains exactly 2 copies of each digit of k.
%C A114258 From _Chai Wah Wu_, Feb 27 2024: (Start)
%C A114258 If k is a term, then k == 0 (mod 9) or k == 2 (mod 9) (see A370676).
%C A114258 First decimal digit of each term is 3 or larger. (End)
%H A114258 Chai Wah Wu, <a href="/A114258/b114258.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..645 from Seiichi Manyama)
%e A114258 72576 is in the sequence since its square 5267275776 contains four 7's, two 2's, two 5's and two 6's.
%o A114258 (Python)
%o A114258 from math import isqrt
%o A114258 from itertools import count, islice
%o A114258 def A114258_gen(): # generator of terms
%o A114258     for l in count(1):
%o A114258         a = isqrt(10**((l<<1)-1))
%o A114258         if (a9:=a%9):
%o A114258             a -= a9
%o A114258         for b in range(a,10**l,9):
%o A114258             for c in (0,2):
%o A114258                 k = b+c
%o A114258                 if sorted(str(k)*2)==sorted(str(k**2)):
%o A114258                     yield k
%o A114258 A114258_list = list(islice(A114258_gen(),20)) # _Chai Wah Wu_, Feb 27 2024
%Y A114258 Cf. A114259, A114260, A114261, A199630.
%Y A114258 Cf. A061656, A061657, A061658, A061659, A061660, A061661, A061662, A061663, A061664.
%K A114258 base,nonn
%O A114258 1,1
%A A114258 _Giovanni Resta_, Nov 18 2005