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A293752
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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 tau (the golden ratio, (1+sqrt(5))/2).
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4
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4, 142, 144, 156, 158, 160, 192, 220, 222, 226, 228, 230, 276, 278, 310, 312, 314, 334, 340, 358, 360, 374, 376, 380, 390, 394, 628, 662, 664, 672, 678, 680, 682, 684, 686, 692, 694, 700, 718, 720, 722, 740, 1666, 1670, 1674, 1688, 1690, 1692, 1698, 1724
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OFFSET
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1,1
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COMMENTS
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This sequence together with A293754 and A293755 partition the positive integers.
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LINKS
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Table of n, a(n) for n=1..50.
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EXAMPLE
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In base 2, tau = 1.10011110001101110111100..., so that the initial segment
1.100, of length 4 is the first segment to have the same number of 0's and 1's, so that a(1) = 4.
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MATHEMATICA
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z = 300; u = N[GoldenRatio, 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[Range[z], c[0, #] == c[1, #] &] (* A293752 *)
u/2 (* A293753 *)
Select[Range[z], c[0, #] < c[1, #] &] (* A293754 *)
Select[Range[z], c[0, #] > c[1, #] &] (* A293755 *)
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CROSSREFS
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Cf. A068432, A293753, A293754, A293755.
Sequence in context: A299722 A210831 A247483 * A299833 A231949 A239248
Adjacent sequences: A293749 A293750 A293751 * A293753 A293754 A293755
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KEYWORD
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nonn,easy,base
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AUTHOR
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Clark Kimberling, Oct 18 2017
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STATUS
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approved
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