OFFSET
1,2
COMMENTS
The original name was "Generalized FibCon sequence". However, this sequence has only a passing resemblance to Connell-like sequences (see A001614 and the paper by Iannucci & Mills-Taylor), which are all monotone, while this sequence is a bijection of natural numbers.
LINKS
Douglas E. Iannucci, Donna Mills-Taylor, On Generalizing the Connell Sequence, Journal of Integer Sequences, Vol. 2 (1999), Article 99.1.7
FORMULA
If n < 4, a(n) = n. If n = A000045(A072649(n)+1), then a(n) = a(n-1-A000045(A072649(n)))+3, otherwise a(n) = a(n-1)+3. - Antti Karttunen, Oct 05 2009.
1. The sequence is formed by concatenating subsequences S0,S1, S2, ..., each of finite length. 2. The subsequence S0 consists of the element 1. 3. The n-th subsequence has F(n) elements, F(n) denotes n-th Fibonacci number. 4. Each subsequence is nondecreasing and the difference between two consecutive elements in the same subsequence is 3.
EXAMPLE
1,4,7,10,13,16,19,22,25,28,31,...
2,5,8,11,14,17,20,23,26,29,32,...
3,6,9,12,15,18,21,24,27,30,33,...
then
S0={1}
S1={2}
S2={3,6}
S3={4,7,10}
S4={5,8,11,14,17}
S5={9,12,15,18,21,24,27,30}
...
and concatenating S0/S1/S2/S3/S4/S5/... gives this sequence.
PROG
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Ctibor O. Zizka, May 14 2008
EXTENSIONS
Edited, extended, starting offset changed from 0 to 1, and Scheme-code added by Antti Karttunen, Oct 05 2009
STATUS
approved