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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.
1
0, 1, 351, 379, 496, 558, 639, 1495, 1792, 3259, 4600, 5950, 6399, 6588, 8568, 10494, 10495, 12799, 17380, 17919, 26479, 38872, 38880, 44991, 44992, 46585, 48888, 56952, 59247, 60895, 64639, 89839, 89848, 89856, 92799, 105390, 142848, 168895, 174078, 179596
OFFSET
1,3
COMMENTS
Intersection of A077436 and A058369.
Numbers such that A007953(n) = A007953(n^2) and A000120(n) = A000120(n^2).
LINKS
EXAMPLE
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.
MATHEMATICA
Select[Range[0, 180000], Total[IntegerDigits[#]]==Total[IntegerDigits[#^2]]&&Total[ IntegerDigits[ #, 2]]==Total[IntegerDigits[#^2, 2]]&] (* Harvey P. Dale, May 29 2023 *)
PROG
(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())]
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Tom Edgar, Aug 27 2015
EXTENSIONS
Name (definition) and Example edited by Harvey P. Dale, May 29 2023
STATUS
approved