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A270743 Runlength sequence of the zero-one sequence A270742. 2
1, 1, 2, 1, 2, 4, 1, 3, 6, 1, 4, 8, 1, 5, 10, 1, 6, 12, 1, 7, 14, 1, 8, 16, 1, 9, 18, 1, 10, 20, 1, 11, 22, 1, 12, 24, 1, 13, 26, 1, 14, 28, 1, 15, 30, 1, 16, 32, 1, 17, 34, 1, 18, 36, 1, 19, 38, 1, 20, 40, 1, 21, 42, 1, 22, 44, 1, 23, 46, 1, 24, 48, 1, 25 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This is the runlength sequence for C = (1/2)*(3/4)*(7/8)*(15/16)... in each base (2,3,4,...); for base 10, we have C = 0.8900100999989990000001000..., as in A132038.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000

FORMULA

a(3n) = 2n for n > 0, a(3n+1) = 1 for n >= 0, a(3n+2) = n + 1 for n >= 0.

EXAMPLE

(zero-one sequence at A270742) = (0, 1, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0,...), with first 6 runs 0, 1, 00, 1, 00, 1111 of lengths 1,1,2,1,2,4.

MATHEMATICA

d = Join[{0}, RealDigits[QPochhammer[1/2], 2, 200000][[1]]];

u = Map[Length, Split[d]]

CROSSREFS

Cf.  A132038, A270742.

Sequence in context: A087704 A165092 A306915 * A209750 A156042 A287691

Adjacent sequences:  A270740 A270741 A270742 * A270744 A270745 A270746

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Apr 04 2016

STATUS

approved

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Last modified December 15 09:05 EST 2019. Contains 329995 sequences. (Running on oeis4.)