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A278920
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In the binary race of Pi, where the race leader changes.
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4
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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