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A136277 From the binary representation of n: binomial(number of ones, number of blocks of contiguous ones). 5
1, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 3, 2, 3, 3, 4, 1, 1, 1, 3, 1, 1, 3, 6, 2, 3, 3, 6, 3, 6, 4, 5, 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 4, 3, 4, 6, 10, 2, 3, 3, 6, 3, 4, 6, 10, 3, 6, 6, 10, 4, 10, 5, 6, 1, 1, 1, 3, 1, 1, 3, 6, 1, 1, 1, 4, 3, 4, 6, 10, 1, 1, 1, 4, 1, 1, 4, 10, 3, 4, 4, 10, 6, 10, 10, 15, 2, 3, 3, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

First occurrence of k: 1, 3, 7, 15, 31, 23, 127, 255, 511, 47, 2047, 4095, 8191, 16383, 95, 65535, 131071, ..., . k must occur by 2^k-1. - Robert G. Wilson v

Record values: 1, 3, 7, 15, 23, 47, 95, 175, 191, 351, 703, 1375, 1407, 2751, 5503, 10943, 11007, 21887, 22015, 43775, 87423, 87551, 174847, 175103, 349695, 699135, 699391, 1398271, 1398783, 2796543, 2797567, 5592575, 5593087, 11185151, 11186175, ..., . - Robert G. Wilson v

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A007318(A000120(n),A069010(n)). - R. J. Mathar, Apr 01 2008

a(n) = A181591(A005940(1+n)). - Antti Karttunen, May 29 2017

MAPLE

A000120 := proc(n) local i ; add(i, i=convert(n, base, 2)) ; end: A069010 := proc(n) local b, c, i ; if n = 0 then RETURN(0) ; fi ; b := convert(n, base, 2) ; c := 0 ; if nops(b) > 1 then for i from 1 to nops(b) do if op(i, b) <> op(i-1, b) then c := c+1 ; fi ; od: fi ; op(1, b)+floor(c/2) ; end: A136277 := proc(n) binomial(A000120(n), A069010(n)) ; end: seq(A136277(n), n=0..120) ; # R. J. Mathar, Apr 01 2008

MATHEMATICA

f[n_] := Block[{id = IntegerDigits[n, 2]}, Binomial[ Count[id, 1], Floor[(Length@ Split@ id + 1)/2]]]; Array[f, 100] (* Robert G. Wilson v *)

CROSSREFS

Cf. A000120, A007318, A069010, A107345, A181591, A278222.

Sequence in context: A232186 A325757 A161161 * A133233 A174430 A116361

Adjacent sequences:  A136274 A136275 A136276 * A136278 A136279 A136280

KEYWORD

nonn,easy

AUTHOR

Neven Juric (neven.juric(AT)apis-it.hr), Apr 01 2008

EXTENSIONS

More terms from R. J. Mathar and Robert G. Wilson v, Apr 01 2008

STATUS

approved

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Last modified October 23 19:37 EDT 2019. Contains 328373 sequences. (Running on oeis4.)