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Search: id:A027581
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| A027581 |
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Sequence satisfies T(T(a))=a, where T is defined below. |
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+0
2
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| 1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 17, 21, 26, 30, 36, 43, 49, 58, 69, 79, 91, 106, 122, 140, 161, 183, 209, 239, 271, 308, 348, 392, 444, 501, 561, 630, 708, 791, 884, 989, 1101, 1225, 1365, 1516, 1681, 1863, 2062, 2282, 2522, 2782, 3069, 3381, 3719, 4092
(list; graph; listen)
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OFFSET
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0,4
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REFERENCES
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S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, Nov 15 1996
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LINKS
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M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210.
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FORMULA
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Define T:a->b by: given a0<=a1<=..., remove duplicates, keep only odd numbers, getting c0<c1<...; define b0, b1, b2, ... by Sum bi*x^i = Product 1/(1-x^ci). - Description corrected by and more terms from Michael Somos, Apr 27 2003.
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EXAMPLE
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1+1x+1x^2+2x^3+2x^4+3x^5+4x^6+5x^7+6*x^8+8*x^9+10*x^10+12*x^11+15*x^12+... = 1/((1-x^1)(1-x^3)(1-x^5)(1-x^7)(1-x^9)(1-x^11)(1-x^15)(1-x^17)(1-x^21)...)
1+1x+1x^2+2x^3+2x^4+3x^5+4x^6+4x^7+5*x^8+6*x^9+7*x^10+8*x^11+9*x^12+... = 1/((1-x^1)(1-x^3)(1-x^5)(1-x^15)(1-x^17)(1-x^21)...)
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CROSSREFS
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Cf. A027582=T(a).
Sequence in context: A083847 A034142 A008675 this_sequence A058706 A034143 A034144
Adjacent sequences: A027578 A027579 A027580 this_sequence A027582 A027583 A027584
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KEYWORD
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nonn,easy,eigen
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Description corrected by and more terms from Michael Somos, Apr 27 2003.
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