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A308782
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Index of first occurrence of n appearing twice in succession in van Eck's sequence (A181391), or 0 if it never occurs.
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1
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2, 0, 8, 50, 132, 414, 171, 659, 96, 361, 12311, 7224, 5896, 2954, 5804, 72387, 12756, 1292, 4332, 3715, 2704, 1887, 5780, 9837, 11721, 1094, 70067, 32610, 57658, 26146, 167389, 94957, 36588, 19663, 35588, 9627, 108296, 51653, 38147, 54788, 81871, 15502
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OFFSET
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0,1
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COMMENTS
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With V=A181391, a(n) is the smallest number m such that V(m) = V(m-1) = n.
Since van Eck's sequence is generated by considering the gap between identical terms reappearing, it is of interest to consider terms of value n which repeat with a gap of length n.
When this happens the term is repeated in succession.
Some observations that follow from the definition of V:
V(a(n)-1-n) = n. The value n has to appear exactly n terms apart in V to make the following term equal to n, e.g., for n=3: "..., 3, 8, 0, 3, 3, ...".
V(a(n)+1) = 1. Since the term n appeared twice in a row, the following term of V must be 1.
V(a(n)-2) = V(a(n)-n-2) = V(a(n)-2*n-2). The number preceding the repeated terms appears three times with gaps of n.
V(a(n)+2) = the number of terms since the previous repeated value of some number (though it may not be the first time it is repeated). So V(a(n)-V(a(n)+2)) = V(a(n)-V(a(n)+2)-1).
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LINKS
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EXAMPLE
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V(95) = V(96) = 8. Therefore, a(8) = 96.
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V(a(n)-1-n) = n:
a(8) - 1 - 8 = 87.
V(87) = 8.
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V(a(n)+1) = 1:
a(8) + 1 = 97.
V(97) = 1.
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V(a(n)-2) = V(a(n)-n-2) = V(a(n)-2*n-2):
a(8) - 2 = 94.
a(8) - 8 - 2 = 86.
a(8) - 2*8 - 2 = 78.
V(94) = V(86) = V(78) = 3.
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V(a(8)+2) = 46. a(8) - 46 = 50. The previous repeated terms in V are V(50) = V(49) = 5.
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PROG
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(C++) See Links section.
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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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