A027582 Sequence satisfies T(T(a))=a, where T is defined below.

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

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