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A293725
Numbers k such that c(k,0) = c(k,1), where c(k,d) = number of d's in the first k 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
OFFSET
1,1
COMMENTS
This sequence together with A293727 and A293728 partition the positive integers.
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
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Oct 16 2017
STATUS
approved