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.

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

Author

Tom Edgar, Aug 27 2015

Keywords

• nonn
• base

Comments

Intersection of A077436 and A058369.

Numbers such that A007953(n) = A007953(n^2) and A000120(n) = A000120(n^2).

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A077436, A058369, A007953, A000120.

Programs

Mathematica

Select[Range[0,180000],Total[IntegerDigits[#]]==Total[IntegerDigits[#^2]]&&Total[ IntegerDigits[ #,2]]==Total[IntegerDigits[#^2,2]]&] (* Harvey P. Dale, May 29 2023 *)

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())]

Extensions

Name (definition) and Example edited by Harvey P. Dale, May 29 2023