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

Author

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

Keywords

• nonn

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.

Examples

			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.
		

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

Crossrefs

Cf. A004601, A039624, A166006.

Programs

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