A342727 Digitally balanced numbers in base i-1: numbers that in base i-1 have the same number of 0's as 1's.

2, 21, 26, 31, 36, 41, 46, 51, 310, 315, 325, 330, 335, 340, 345, 350, 355, 360, 365, 370, 375, 390, 395, 405, 410, 415, 420, 425, 430, 435, 455, 470, 475, 485, 490, 495, 535, 550, 555, 565, 570, 575, 580, 585, 590, 595, 600, 605, 610, 620, 625, 630, 635, 645

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Walter Penney, A "binary" system for complex numbers, Journal of the ACM, Vol. 12, No. 2 (1965), pp. 247-248.

Example

2 is a term since its representation in base i-1, 1100, has 2 0's and 2 1's.
21 is a term since its representation in base i-1, 110011010001, has 6 0's and 6 1's.

Mathematica

v = {{0, 0, 0, 0}, {0, 0, 0, 1}, {1, 1, 0, 0}, {1, 1, 0, 1}}; balQ[n_] := Plus @@ (d = IntegerDigits[n]) == Length[d]/2; q[n_] := balQ @ FromDigits[Flatten@v[[1 + Reverse @ Most[Mod[NestWhileList[(# - Mod[#, 4])/-4 &, n, # != 0 &], 4]]]]]; Select[Range[1000], q]

Crossrefs

Cf. A066321, A066323, A271472, A342725, A342726, A342728, A342729.

Similar sequences: A031443 (binary), A210619 (Zeckendorf).

Sequence in context: A135053 A042565 A079907 * A075715 A326735 A294377

Adjacent sequences: A342724 A342725 A342726 * A342728 A342729 A342730

Keyword

nonn,base

Author

Amiram Eldar, Mar 19 2021

Status

approved