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Search: id:A136496
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| A136496 |
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Solution of the complementary equation b(n)=a(a(n))+n; this is sequence b; sequence a is A136495. |
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+0
3
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| 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
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OFFSET
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1,1
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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, A136495.
Adjacent sequences: A136493 A136494 A136495 this_sequence A136497 A136498 A136499
Sequence in context: A053663 A022430 A079418 this_sequence A076991 A130205 A054067
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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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