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A136495
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Solution of the complementary equation b(n)=a(a(n))+n.
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4
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1, 3, 4, 5, 7, 9, 10, 12, 13, 14, 16, 17, 18, 20, 22, 23, 24, 26, 28, 29, 31, 32, 33, 35, 37, 38, 40, 41, 42, 44, 45, 46, 48, 50, 51, 53, 54, 55, 57, 58, 59, 61, 63, 64, 65, 67, 69, 70, 72, 73, 74, 76, 77, 78, 80, 82, 83, 84, 86, 88, 89, 91, 92, 93, 95, 97, 98, 100, 101, 102
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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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).
A005374(a(n)) = n. [Reinhard Zumkeller, Dec 17 2011]
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REFERENCES
| Clark Kimberling and Peter 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.
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Hofstadter H-Sequence.
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FORMULA
| Let Z = (3rd order Zeckendorff 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.
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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.
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PROG
| (Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a136495 n = (fromJust $ n `elemIndex` tail a005374_list) + 1
-- Reinhard Zumkeller, Dec 17 2011
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CROSSREFS
| Cf. A020942, A035513, A136189, A136496.
Sequence in context: A047251 A183213 A183172 * A184419 A189665 A156246
Adjacent sequences: A136492 A136493 A136494 * A136496 A136497 A136498
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu), Jan 01 2008
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