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A027582 Sequence satisfies T(T(a))=a, where T is defined below. 1
1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 9, 10, 11, 14, 15, 17, 20, 21, 25, 29, 31, 35, 39, 43, 48, 53, 57, 62, 70, 75, 82, 90, 96, 106, 116, 124, 135, 146, 157, 170, 184, 197, 211, 229, 244, 262, 282, 300, 322, 346, 368, 393, 420, 447, 476, 508, 539, 572, 611, 646, 685 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

REFERENCES

S. Viswanath (student, Dept. Math, Indian Inst. Technology, Kanpur) A Note on Partition Eigensequences, preprint, Nov 15 1996.

LINKS

Table of n, a(n) for n=0..62.

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

M. Bernstein and N. J. A. Sloane, Some canonical sequences of integers, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

FORMULA

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, May 04 2003.

EXAMPLE

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)...)

CROSSREFS

Cf. A027581=T(a).

Sequence in context: A211524 A008672 A097923 * A259198 A011880 A029044

Adjacent sequences:  A027579 A027580 A027581 * A027583 A027584 A027585

KEYWORD

nonn,easy,eigen

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)