A136496 Solution of the complementary equation b(n)=a(a(n))+n; this is sequence b; sequence a is A136495.

2, 6, 8, 11, 15, 19, 21, 25, 27, 30, 34, 36, 39, 43, 47, 49, 52, 56, 60, 62, 66, 68, 71, 75, 79, 81, 85, 87, 90, 94, 96, 99, 103, 107, 109, 113, 115, 118, 122, 124, 127, 131, 135, 137, 140, 144, 148, 150, 154, 156, 159, 163, 165, 168, 172, 176, 178, 181, 185, 189

Offset

1,1

Comments

b = 1 + (column 1 of Z) = 1 + A020942. The pair (a,b) also satisfy the following complementary equations: b(n)=a(a(a(n)))+1; a(b(n))=a(n)+b(n); b(a(n))=a(n)+b(n)-1; (and others).

References

Clark Kimberling and Peter J. C. Moses, Complementary equations and Zeckendorf arrays, in Applications of Fibonacci Numbers, vol.10, Proceedings of the Thirteenth International Conference on Fibonacci Numbers and Their Applications, William Webb, editor, Congressus Numerantium, Winnipeg, Manitoba 201 (2010) 161-178.

Links

Table of n, a(n) for n=1..60.

Formula

Let Z = (3rd order Zeckendorf array) = A136189. Then a = ordered union of columns 1,3,4,6,7,9,10,12,13,... of Z, b = ordered union of columns 2,5,8,11,14,... of Z.

Example

b(1) = a(a(1))+1 = a(1)+1 = 1+1 = 2;
b(2) = a(a(2))+2 = a(3)+2 = 4+2 = 6;
b(3) = a(a(3))+3 = a(4)+3 = 5+3 = 8;
b(4) = a(a(4))+4 = a(5)+4 = 7+4 = 11.

Crossrefs

Cf. A020942, A035513, A136189, A136495.

Sequence in context: A067246 A370866 A184420 * A183173 A178931 A243184

Adjacent sequences: A136493 A136494 A136495 * A136497 A136498 A136499

Keyword

nonn

Author

Clark Kimberling, Jan 01 2008

Status

approved