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Search: id:A114990
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| 1, 1, 2, 2, 3, 5, 8, 6, 11, 17, 28, 24, 31, 55, 86, 98, 135, 233, 368, 256, 369, 625, 994, 1122, 1555, 2677, 4232, 3206, 5835, 9041, 14876, 12760, 16471, 29231, 45702, 52082, 71743, 123825, 195568, 136048, 204071, 340119, 544190, 612214, 850297, 1462511
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OFFSET
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1,3
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COMMENT
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The sequence is clearly not monotonic, however the subsequences of even terms and of odd terms are each strictly increasing. The sequence is obviously bounded above by the fibonacci sequence. The subsequence of n-th terms, where n is congruent to 2 or 3 mod 4, is bounded below by the fibonacci sequence; therefore a(2n)>f(n) for n>1. - Joseph Pedersen (jmp456(AT)psu.edu), Feb 27 2006
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FORMULA
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a(1)=a(2)=1; a(n)=a(n-2)+A000265(a(n-1)) - Joseph Pedersen (jmp456(AT)psu.edu), Feb 27 2006
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EXAMPLE
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The highest odd integer dividing a(11)=28 is 7. So a(12) = a(10) + 7 = 17 + 7 = 24.
The greatest odd divisor of a(11)=28 is 7, so a(12)= a(10)+7 = 17+7 = 24.
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CROSSREFS
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Cf. A000265.
Sequence in context: A062724 A126024 A127678 this_sequence A111181 A076777 A111123
Adjacent sequences: A114987 A114988 A114989 this_sequence A114991 A114992 A114993
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KEYWORD
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easy,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.com), Feb 22 2006
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EXTENSIONS
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More terms from Joseph Pedersen (jmp456(AT)psu.edu) and Amy Postell (arp179(AT)psu.edu), Feb 27 2006
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