OFFSET
1
COMMENTS
3 + a(n) is almost, but not quite, the length of consecutive runs of same-sign numbers in A088137(m) starting at m=1. To be precise, A088137(m) for m>0 is 1, 2, 1, -4, -11, -10, 13, 56, 73, -22, -263, -460, -131, 1118, 2629, 1904,... which has 3 positive numbers, 3 negative numbers, 3 positive, 4 negative, ... giving the sequence 3,3,3,4, 3,3,4, 3,3,3,4, ..., and aside from that first "3" this is an almost perfect match for 3 + a(n) which begins 4,3,3,4, 3,3,4, 3,3,3,4, ... . Aside from that first term, these two sequences first differ at the 97th term, and differ only 23 times more in the first 400 terms. - Greg Dresden, Oct 06 2019
LINKS
Clark Kimberling, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 1 - floor((n+1)*(1-1/r)) + floor(n*(1-1/r)), where r = sqrt(12). [corrected by Georg Fischer, Sep 01 2022]
MATHEMATICA
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 15 2017
STATUS
approved