A027581 - OEIS

%I #11 May 07 2017 22:37:07

%S 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,

%T 122,140,161,183,209,239,271,308,348,392,444,501,561,630,708,791,884,

%U 989,1101,1225,1365,1516,1681,1863,2062,2282,2522,2782,3069,3381,3719,4092

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

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

%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%F 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.

%e 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)...)

%e 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)...)

%Y Cf. A027582=T(a).

%K nonn,easy,eigen

%O 0,4

%A _N. J. A. Sloane_.

%E Description corrected by and more terms from _Michael Somos_, Apr 27 2003.