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A184750
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a(n) = largest k such that A000326(n+1) = A000326(n) + (A000326(n) mod k), or 0 if no such k exists.
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3
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0, 0, 0, 0, 19, 32, 48, 67, 89, 114, 142, 173, 207, 244, 284, 327, 373, 422, 474, 529, 587, 648, 712, 779, 849, 922, 998, 1077, 1159, 1244, 1332, 1423, 1517, 1614, 1714, 1817, 1923, 2032, 2144, 2259, 2377, 2498, 2622, 2749
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OFFSET
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1,5
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COMMENTS
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From the definition, a(n) = A000326(n) - A016777(n) if A000326(n) - A016777(n) > A016777(n), 0 otherwise, where A000326 are the pentagonal numbers and A016777 are the gaps between pentagonal numbers: 3n + 1.
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LINKS
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Rémi Eismann, Table of n, a(n) for n = 1..1000
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FORMULA
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a(n) = 3(n^2-7n-2)/2 for n >= 5 and a(n) = 0 for n <= 4.
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EXAMPLE
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For n = 3 we have A000326(3) = 12, A000326(4) = 22; there is no k such that 22 - 12 = 10 = (12 mod k), hence a(3) = 0.
For n = 5 we have A000326(5) = 35, A000326(6) = 51; 19 is the largest k such that 51 - 35 = 16 = (35 mod k), hence a(5) = 19; a(5) = (75-35-2)/2 = 19.
For n = 25 we have A000326(25) = 925, A000326(26) = 1001; 849 is the largest k such that 1001 - 925 = 76 = (925 mod k), hence a(25) = 849; a(25) = (1875-175-2)/2 = 849.
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CROSSREFS
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Cf. A000326, A016777, A133151, A184751, A117078, A117563, A001223, A118534.
Sequence in context: A146659 A160220 A133151 * A101063 A061962 A116168
Adjacent sequences: A184747 A184748 A184749 * A184751 A184752 A184753
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KEYWORD
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nonn,easy
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AUTHOR
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Rémi Eismann, Jan 21 2011
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STATUS
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approved
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