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A046834 Internal digits of n^2 include digits of n as subsequence.

%I A046834 #25 Apr 04 2023 15:40:36
%S A046834 50,60,250,500,600,760,1050,2050,2500,3050,3628,3710,3760,3792,4050,
%T A046834 4410,5000,5010,5050,5060,5250,6000,6010,6050,6250,6760,7050,7560,
%U A046834 7600,8050,8250,8260,8882,9050,9460,10050,10500,14650,14651,20050,20500
%N A046834 Internal digits of n^2 include digits of n as subsequence.
%C A046834 If n is a member then so is 10*n. - _Robert Israel_, May 07 2020
%H A046834 David A. Corneth, <a href="/A046834/b046834.txt">Table of n, a(n) for n = 1..10000</a> (first 5000 terms from Robert Israel)
%e A046834 a(7) = 1050 is a term because 1050^2 = 1102500; remove the first and last to get internal digits 10250, and 1050 is a subsequence of 10250. - _Robert Israel_, May 07 2020
%p A046834 filter:= n -> StringTools:-IsSubSequence(sprintf("%d",n),sprintf("%d",n^2)[2..-2]):
%p A046834 select(filter, [$10..30000]); # _Robert Israel_, May 07 2020
%o A046834 (Python)
%o A046834 from itertools import count, islice
%o A046834 def A046834_gen(startvalue=1): # generator of terms >= startvalue
%o A046834     for k in count(max(startvalue,1)):
%o A046834         c = iter(str(k**2)[1:-1])
%o A046834         if all(map(lambda b:any(map(lambda a:a==b,c)),str(k))):
%o A046834             yield k
%o A046834 A046834_list = list(islice(A046834_gen(),20)) # _Chai Wah Wu_, Apr 03 2023
%Y A046834 Cf. A046831, A052212.
%K A046834 nonn,base,easy
%O A046834 1,1
%A A046834 _David W. Wilson_