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 A293752 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). 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This sequence together with A293754 and A293755 partition the positive integers. LINKS Table of n, a(n) for n=1..50. EXAMPLE 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. MATHEMATICA 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 *) CROSSREFS Cf. A068432, A293753, A293754, A293755. Sequence in context: A299722 A210831 A247483 * A299833 A231949 A239248 Adjacent sequences: A293749 A293750 A293751 * A293753 A293754 A293755 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Oct 18 2017 STATUS approved

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Last modified May 30 07:09 EDT 2023. Contains 363045 sequences. (Running on oeis4.)