A027581 Sequence satisfies T(T(a))=a, where T is defined below.

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

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..56.

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, Apr 27 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. A027582=T(a).

Sequence in context: A083847 A034142 A008675 * A058706 A034143 A309999

Adjacent sequences: A027578 A027579 A027580 * A027582 A027583 A027584

Keyword

nonn,easy,eigen

Author

N. J. A. Sloane.

Extensions

Description corrected by and more terms from Michael Somos, Apr 27 2003.

Status

approved