A169740 -id:A169740 - cp's OEIS frontend

A030068 The "semi-Fibonacci numbers": a(n) = A030067(2n - 1), where A030067 is the semi-Fibonacci sequence.

1, 2, 3, 5, 6, 9, 11, 16, 17, 23, 26, 35, 37, 48, 53, 69, 70, 87, 93, 116, 119, 145, 154, 189, 191, 228, 239, 287, 292, 345, 361, 430, 431, 501, 518, 605, 611, 704, 727, 843, 846, 965, 991, 1136, 1145, 1299, 1334, 1523, 1525, 1716, 1753, 1981, 1992, 2231, 2279, 2566

Offset: 1

David W. Wilson

Also the unique values of A030067 sorted. - Ralf Stephan, Oct 28 2013
Also, the subsequence of record values of the semi-Fibonacci sequence A030067.
The first differences of this sequence give back A030067. - It is more natural to use offset 1 and a(n) = A060037(2n-1), rather than 0 and a(n) = A060037(2n+1): First, a set should have this offset, and this is indeed the set of values or the range of A030067, i.e., the set of semi-Fibonacci numbers. Second, A060037 also starts at index 1. Third, the sequence A284282(n) = (k such that A030067(2k-1)=n or 0 if there's no such k) is then the characteristic function of this sequence, with nonzero values read as 1. - M. F. Hasler, Mar 24 2017

N. J. A. Sloane, Table of n, a(n) for n = 1..10001

Cf. A030067. Bisections: A169739, A169740.

f[1] = 1; f[n_?EvenQ] := f[n] = f[n/2]; f[n_?OddQ] := f[n] = f[n-1] + f[n-2]; a[n_] := f[2*n+1]; Table[a[n], {n, 1, 55}] (* Jean-François Alcover, Jul 16 2015 *)

A030068_vec=[1,2,3]; A030068(n)={n>#A030068_vec&&for(n=#A030068_vec,-1+#A030068_vec=concat(A030068_vec,vector(n-#A030068_vec)),A030068_vec[n+1]=A030068_vec[n]+A030067(n));A030068_vec[n]} \\ M. F. Hasler, Mar 24 2017

Vec(prod(k=0,5,1/Ser(x^2^k)+x^2^k)) \\ Correct for n < 2*2^5. - M. F. Hasler, Mar 27 2017

G.f.: x*(r(x) * r(x^2) * r(x^4) * r(x^8) * ...) where r(x) is (1 + 2x + x^2 + x^3 + x^4 + x^5 + ...). - Gary W. Adamson, Sep 02 2016

a(n+1) = a(n) + A060037(n). The above g.f. can be written as x*Product_{k=0,oo} (1/(1-x^2^k)+x^2^k). - M. F. Hasler, Mar 27 2017

Offset changed to 1 by N. J. A. Sloane, Mar 27 2017

A169739 a(n) = A030068(4n+1).

Original entry on oeis.org

1, 3, 6, 11, 17, 26, 37, 53, 70, 93, 119, 154, 191, 239, 292, 361, 431, 518, 611, 727, 846, 991, 1145, 1334, 1525, 1753, 1992, 2279, 2571, 2916, 3277, 3707, 4138, 4639, 5157, 5762, 6373, 7077, 7804, 8647, 9493, 10458, 11449, 12585, 13730, 15029, 16363, 17886, 19411

Offset: 0

N. J. A. Sloane, May 02 2010

nonn

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

Cf. A030067, A030068, A169740.

f[1]=1; f[n_?EvenQ]:=f[n]=f[n/2]; f[n_?OddQ]:=f[n]=f[n-1]+f[n-2]; a[n_]:=f[2*n+1]; Table[a[n], {n, 0, 100, 2}] (* Vincenzo Librandi, May 27 2019 *)

a(n) = A030067(4n-3). - George Beck, Jan 18 2020

cp's OEIS Frontend

A030068 The "semi-Fibonacci numbers": a(n) = A030067(2n - 1), where A030067 is the semi-Fibonacci sequence.

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