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A030067
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Semi-Fibonacci numbers: a(1) = 1; a(n) = a(n/2) (n even); a(n) = a(n-1)+a(n-2) (n odd).
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14
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1, 1, 2, 1, 3, 2, 5, 1, 6, 3, 9, 2, 11, 5, 16, 1, 17, 6, 23, 3, 26, 9, 35, 2, 37, 11, 48, 5, 53, 16, 69, 1, 70, 17, 87, 6, 93, 23, 116, 3, 119, 26, 145, 9, 154, 35, 189, 2, 191, 37, 228, 11, 239, 48, 287, 5, 292, 53, 345, 16, 361, 69, 430, 1, 431, 70, 501, 17, 518, 87, 605, 6, 611, 93
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| a(2n+1) >= a(2n-1)+1 is monotonically increasing. a(2n)/n can be arbitrarily small, as a(2^n) = 1. - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 28 2006
There are probably an infinite number of primes in the sequence. - Jonathan Vos Post (jvospost3(AT)gmail.com), Mar 28 2006
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
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FORMULA
| Theorem: a(2n+1)-a(2n-1)=a(n). Proof: a(2n+1)-a(2n-1) = a(2n)+a(2n-1)-a(2n-2)-a(2n-3) = a(n)-a(n-1)+a(n-1) (induction) = a(n). - N. J. A. Sloane, May 02 2010
a(2^n - 1) = A129092(n) for n>=1, where A129092 forms the row sums and column 0 of triangle A129100, which is defined by the nice property that column 0 of matrix power A129100^(2^k) = column k of A129100 for k>0. [From Paul D. Hanna (pauldhanna(AT)juno.com), Dec 03 2008]
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MAPLE
| f:=proc(n) option remember; if n=1 then RETURN(1) elif n mod 2 = 0 then RETURN(f(n/2)) else RETURN(f(n-1)+f(n-2)); fi; end;
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CROSSREFS
| Cf. A000045, A030068, A074364.
Cf. A129092, A129100. [From Paul D. Hanna (pauldhanna(AT)juno.com), Dec 03 2008]
See A109671 for a variant.
Sequence in context: A116529 A169747 A064989 * A181363 A105800 A105602
Adjacent sequences: A030064 A030065 A030066 * A030068 A030069 A030070
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KEYWORD
| nonn,nice
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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