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A330359
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Race of lucky numbers of the form 4*k - 1 vs. 4*k + 1 is tied at the a(n)-th lucky number.
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2
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2, 4, 6, 16, 20, 22, 24, 2684, 2686, 2688, 2696, 2710, 2712, 109978, 110026, 110028, 110030, 110052, 110056, 110060, 110068, 110070, 110154, 110156, 110158, 110160, 118048, 118050, 118126, 118128, 118130, 118132, 118134, 118136, 118138, 118152, 118154, 118156
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OFFSET
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1,1
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COMMENTS
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All the terms are even by definition. For each term m, there are m/2 lucky numbers of the form 4*k - 1 and m/2 lucky numbers of the form 4*k + 1 up to the m-th lucky number.
Gardiner et al. (1956) noted that the ratio between the numbers of lucky numbers of the form 4*k - 1 and 4*k + 1 seems to tend to 1, with a preponderance, at first, of the lucky numbers of the form 4*k + 3.
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LINKS
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EXAMPLE
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6 is in the sequence since the first 6 lucky numbers are 1, 3, 7, 9, 13, 15, half of them are of the form 4*k-1 (3, 7, 15) and half of the form 4*k+1 (1, 9, 13).
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MATHEMATICA
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lucky = Import["b000959.txt", "Table"][[;; , 2]]; Flatten[Position[Accumulate[ Mod[lucky, 4] - 2], 0]] (* use the b-file from A000959 *)
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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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