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Search: id:A119712
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| A119712 |
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a(k) is the smallest integer n such that the k-th difference of the partition sequence A000041 is positive from n onwards. |
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+0
1
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| 0, 1, 6, 23, 64, 129, 222, 345, 502, 695, 924
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The first entry in considered to be indexed by zero. For example, the third difference A072380 starts with -1,1, and continues alternating in sign till the 24th entry, from which point it is positive.
Using a different definition of the difference operator, this sequence has also been given as 1,8,26,68,134,228,352, etc
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REFERENCES
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I. J. Good, Problem 6137, American Mathematical Monthly 1978 pages 830-831
Hansraj Gupta, Finite Differences of the Partition Function, pp. 1241-1243.
A. M. Odlyzko, Differences of the partition function, Acta Arith., 49 (1988), pp. 237-254
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FORMULA
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Odlyzko gives an asymptotic formula a(k)~(6/(Pi)^2) * (klogk)^2
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CROSSREFS
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Adjacent sequences: A119709 A119710 A119711 this_sequence A119713 A119714 A119715
Sequence in context: A022269 A026817 A009017 this_sequence A005745 A045618 A038737
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KEYWORD
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nonn
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AUTHOR
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Moshe Newman (moshnoiman(AT)gmail.com), Jun 11 2006
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