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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Intersection of A077436 and A058369. Numbers such that A007953(n) = A007953(n^2) and A000120(n) = A000120(n^2). LINKS Giovanni Resta, Table of n, a(n) for n = 1..10000 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 Cf. A077436, A058369, A007953, A000120. Sequence in context: A074203 A045126 A025385 * A292990 A281555 A363422 Adjacent sequences: A261637 A261638 A261639 * A261641 A261642 A261643 KEYWORD nonn,base AUTHOR Tom Edgar, Aug 27 2015 EXTENSIONS Name (definition) and Example edited by Harvey P. Dale, May 29 2023 STATUS approved

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Last modified August 11 08:53 EDT 2024. Contains 375059 sequences. (Running on oeis4.)