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A293725 Numbers n such that c(n,0) = c(n,1), where c(n,d) = number of d's in the first n digits of the base-2 expansion of sqrt(2). 4
2, 10, 20, 24, 28, 32, 318, 328, 330, 334, 336, 608, 622, 636, 638, 674, 676, 678, 680, 682, 826, 828, 832, 836, 838, 842, 844, 846, 848, 850, 852, 856, 858, 876, 880, 884, 886, 898, 906, 908, 918, 920, 928, 930, 942, 944, 946, 948, 950, 962, 964, 966, 968 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence together with A293727 and A293728 partition the positive integers.

LINKS

Table of n, a(n) for n=1..53.

EXAMPLE

In base-2, sqrt(2) = 1.0110101000001001111001..., so that initial segments

1.0; 1.011010100..., of lengths 2,10,... have the same number of 0's and 1's.

MATHEMATICA

z = 300; u = N[Sqrt[2], z]; d = RealDigits[u, 2][[1]];

t[n_] := Take[d, n]; c[0, n_] := Count[t[n], 0]; c[1, n_] := Count[t[n], 1];

Table[{n, c[0, n], c[1, n]}, {n, 1, 100}]

u = Select[-1 + Range[z], c[0, #] == c[1, #] &]  (* A293725 *)

u/2  (* A293726 *)

Select[-1 + Range[z], c[0, #] < c[1, #] &]  (* A293727 *)

Select[-1 + Range[z], c[0, #] > c[1, #] &]  (* A293728 *)

CROSSREFS

Cf. A004539, A002103, A293726, A293727, A293728.

Sequence in context: A306105 A038103 A307254 * A305448 A177150 A165551

Adjacent sequences:  A293722 A293723 A293724 * A293726 A293727 A293728

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Oct 16 2017

STATUS

approved

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Last modified May 26 07:44 EDT 2019. Contains 323579 sequences. (Running on oeis4.)