cp's OEIS Frontend

A261640 Numbers n such that the digital sum of n is the same as the digital sum of n^2 in both base 2 and base 10.

%I A261640 #9 May 29 2023 18:27:04
%S A261640 0,1,351,379,496,558,639,1495,1792,3259,4600,5950,6399,6588,8568,
%T A261640 10494,10495,12799,17380,17919,26479,38872,38880,44991,44992,46585,
%U A261640 48888,56952,59247,60895,64639,89839,89848,89856,92799,105390,142848,168895,174078,179596
%N A261640 Numbers n such that the digital sum of n is the same as the digital sum of n^2 in both base 2 and base 10.
%C A261640 Intersection of A077436 and A058369.
%C A261640 Numbers such that A007953(n) = A007953(n^2) and A000120(n) = A000120(n^2).
%H A261640 Giovanni Resta, <a href="/A261640/b261640.txt">Table of n, a(n) for n = 1..10000</a>
%e A261640 Consider the number n = 351 so n^2 = 123201. The base-10 digit sums of 351 and 123201 are both 9. Moreover, 351 has binary representation 101011111 and 123201 has binary representation 11110000101000001 and both have base-2 digit sum = 7. Thus 351 is a term in the sequence.
%t A261640 Select[Range[0,180000],Total[IntegerDigits[#]]==Total[IntegerDigits[#^2]]&&Total[ IntegerDigits[ #,2]]==Total[IntegerDigits[#^2,2]]&] (* _Harvey P. Dale_, May 29 2023 *)
%o A261640 (Sage) [n for n in [0..200000] if sum((n).digits(2))==sum((n^2).digits(2)) and sum((n).digits())==sum((n^2).digits())]
%Y A261640 Cf. A077436, A058369, A007953, A000120.
%K A261640 nonn,base
%O A261640 1,3
%A A261640 _Tom Edgar_, Aug 27 2015
%E A261640 Name (definition) and Example edited by _Harvey P. Dale_, May 29 2023