login
A020942
First column of 3rd-order Zeckendorf array A136189.
15
1, 5, 7, 10, 14, 18, 20, 24, 26, 29, 33, 35, 38, 42, 46, 48, 51, 55, 59, 61, 65, 67, 70, 74, 78, 80, 84, 86, 89, 93, 95, 98, 102, 106, 108, 112, 114, 117, 121, 123, 126, 130, 134, 136, 139, 143, 147, 149, 153, 155, 158, 162, 164, 167, 171, 175, 177, 180, 184
OFFSET
1,2
COMMENTS
I would like to get similar sequences where the least term in the representation is 2 [gives 2 8 11 15 21 27 30..., which is now A064105], 3, 4, 6, etc. They are the 2nd, 3rd, etc. columns of the 3rd-order Zeckendorf array. [See cross-references. - N. J. A. Sloane, Apr 29 2024]
LINKS
Larry Ericksen and Peter G. Anderson, Patterns in differences between rows in k-Zeckendorf arrays, The Fibonacci Quarterly, Vol. 50, February 2012. - N. J. A. Sloane, Jun 10 2012
Clark Kimberling, The Zeckendorf array equals the Wythoff array, Fibonacci Quarterly 33 (1995) 3-8.
FORMULA
Any number n has unique representation as a sum of terms from {1, 2, 3, 4, 6, 9, 13, 19, ...} (cf. A000930) such that no two terms are adjacent or pen-adjacent; e.g., 7=6+1. Sequence gives all n where that representation involves 1.
Conjecture: a(n) = A202342(n) + n. - Sean A. Irvine, May 05 2019
EXAMPLE
1=1; 5=4+1; 7=6+1; 10=9+1; etc.
CROSSREFS
KEYWORD
nonn,easy,nice
EXTENSIONS
More terms from Naohiro Nomoto, Sep 17 2001
STATUS
approved