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A064827 Numbers k such that each digit of k occurs among the digits of k^2. 4

%I #19 Apr 03 2023 18:23:21

%S 1,5,6,10,11,25,27,50,60,63,64,74,76,95,96,100,101,105,110,125,139,

%T 142,205,250,255,261,270,275,277,278,285,305,364,371,376,405,421,441,

%U 463,472,493,497,500,501,502,503,504,505,506,507,508,509,523,524,525,593,600,601,602

%N Numbers k such that each digit of k occurs among the digits of k^2.

%C That is, if n is d digits long, then each one of those d digits occurs in the digits of n^2.

%e 125^2 = 15625, which contains all digits of 125, so 125 is a term of the sequence.

%e 55 is not here because 55^2 = 3025, which has only one 5.

%t Reap[Do[a = DigitCount[n^2]; b = DigitCount[n]; If[Min[a-b] >= 0, Sow[n]], {n, 1, 10^3}]][[2,1]]

%o (Python)

%o from itertools import count, islice

%o from collections import Counter

%o def A064827_gen(startvalue=1): # generator of terms >= startvalue

%o return filter(lambda k:Counter(str(k))<=Counter(str(k**2)),count(max(startvalue,1)))

%o A064827_list = list(islice(A064827_gen(),20)) # _Chai Wah Wu_, Apr 03 2023

%Y Cf. A046827 (essentially the same).

%K nonn,base

%O 1,2

%A _Joseph L. Pe_, Feb 14 2002

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