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Search: id:A130049
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| A130049 |
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An inductive sum sequence. |
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+0
4
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| 0, 3, 6, 7, 17, 12, 32, 20, 51, 29, 72, 39, 97, 50, 127, 63, 161, 77, 197, 92, 236, 108, 279, 126, 327, 145, 378, 166, 432, 188, 489, 211, 550, 235, 614, 260, 681, 286, 751, 313, 826, 341, 906, 371, 989, 402, 1074, 435, 1162, 469, 1252, 504, 1347, 540, 1445, 577
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OFFSET
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1,2
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COMMENT
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Complement of A130048. The bisection sequences b(1),b(3),b(5),... and b(2),b(4),b(6),... are strictly increasing, but b(2n)<b(2n-1) for n>=3.
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FORMULA
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A130049 is the sequence b defined inductively as follows: Let a(1)=1, a(2)=2, b(1)=0, b(2)=3; for n>=3, let x=Floor(n/2) and y=n-x+1. Then a(n)=least positive integer not among a(1),a(2),...,a(n-1), b(1),b(2),...b(n-1) and b(n)=a(1)+a(2)+...+a(x) if n is even, b(n)=a(y)+a(y+1)+...+a(n) if n is odd.
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EXAMPLE
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(a(1),a(2),...,a(6))=(1,2,4,5,8,9), so x=4 and b(6)=1+2+4+5=12.
(a(1),a(2),...,a(7))=(1,2,4,5,8,9,10), so y=4 and b(7)=5+8+9+10=32.
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CROSSREFS
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Cf. A130048, A130050, A130051.
Sequence in context: A124611 A043305 A072773 this_sequence A056703 A103831 A106357
Adjacent sequences: A130046 A130047 A130048 this_sequence A130050 A130051 A130052
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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), May 03 2007
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