A278920 In the binary race of Pi, where the race leader changes.

1, 7, 17, 33, 6359, 6363, 6371, 6385, 6443, 6445, 6451, 6465, 6525, 6527, 6563, 6565, 6569, 6571, 6573, 6693, 6917, 6923, 6925, 6965, 6967, 7003, 7011, 7337, 7365, 7367, 7369, 7383, 7403, 7705, 7711, 7763, 7769, 7773, 7775, 7789, 7799, 7801, 7809, 7811, 7821, 7823, 7827, 7829, 7855, 7895, 7899

Offset

1,2

Comments

In the binary expansion of Pi (A004601), where the number of zeros and the number of ones exchange the lead.

Obviously a(n) must be odd.

Not necessarily a(n)+1 = A039624(n); although every term here will be one greater than a term in A039624 except the initial one. As a result, this sequence is sparser than A039624.

Links

Hans Havermann and Robert G. Wilson v, Table of n, a(n) for n = 1..823

Hans Havermann, Table of n, a(n) for n = 1..73600

Example

Obviously a(1) = 1 is a term since in the binary expansion of Pi the first binary digit must be a one and therefore the "ones" take the lead.
a(2) = 7 since this is the first time the "zeros" take the lead.
a(3) = 17 since in the first 17 binary digits of Pi, the "ones" regain the count or lead.

Mathematica

pib = RealDigits[Pi, 2, 10000][[1]]; flag = 1; z = o = 0; k = 1; lst = {}; While[k < 10001, If[pib[[k]] == 0, z++, o++]; If[(z > o && flag != 1) || (z < o && flag != -1), AppendTo[lst, k]; flag = -flag]; k++]; lst

Crossrefs

Cf. A004601, A039624, A166006.

Sequence in context: A128002 A301695 A301725 * A074275 A051411 A195016

Adjacent sequences: A278917 A278918 A278919 * A278921 A278922 A278923

Keyword

nonn

Author

Hans Havermann and Robert G. Wilson v, Nov 30 2016

Status

approved