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Search: id:A136495
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| A136495 |
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Solution of the complementary equation b(n)=a(a(n))+n. |
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+0
3
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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; listen)
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OFFSET
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1,2
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COMMENT
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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).
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REFERENCES
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Clark Kimberling and Peter Moses, "Complementary Equations and Zeckendorf Arrays," preprint, 2008.
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FORMULA
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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
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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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CROSSREFS
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Cf. A020942, A035513, A136189, A136496.
Sequence in context: A039017 A153329 A047251 this_sequence A156246 A136014 A112930
Adjacent sequences: A136492 A136493 A136494 this_sequence A136496 A136497 A136498
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jan 01 2008
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