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A342727
Digitally balanced numbers in base i-1: numbers that in base i-1 have the same number of 0's as 1's.
6
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
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
Similar sequences: A031443 (binary), A210619 (Zeckendorf).
Sequence in context: A135053 A042565 A079907 * A075715 A326735 A294377
KEYWORD
nonn,base
AUTHOR
Amiram Eldar, Mar 19 2021
STATUS
approved