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 A136496 Solution of the complementary equation b(n)=a(a(n))+n; this is sequence b; sequence a is A136495. 2
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 15 01:02 EDT 2024. Contains 373402 sequences. (Running on oeis4.)