OFFSET
2,2
COMMENTS
It appears that a(n+1)/a(n) may be converging slowly to 3, but even that it converges is not obvious.
EXAMPLE
a(4) = 5; length 4 sequences are 1,2,4,8; 1,2,4,9; 1,2,5,12; 1,2,5,13; and 1,2,5,14.
PROG
(define (A117294 n) (local ((define (get-ratios seq add?) (cond [(empty? (rest seq)) empty] [else (cons (/ (cond [add? (add1 (first seq))] [else (first seq)]) (second seq)) (get-ratios (rest seq) add?))])) (define (extend-one seq) (local ((define startnext (floor (* (apply max (get-ratios seq false)) (first seq)))) (define endnext (ceiling (* (apply min (get-ratios seq true )) (first seq)))) (define ltodo (build-list (- endnext startnext) (lambda (n) (cons (+ startnext n) seq))))) (cond [(>= (length seq) (sub1 n)) (length ltodo)] [else (apply + (map extend-one ltodo))])))) (extend-one (list 2 1)))) - Joshua Zucker, Jun 05 2006
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Franklin T. Adams-Watters, Apr 26 2006
EXTENSIONS
More terms from Joshua Zucker, Jun 05 2006
Comment edited by Franklin T. Adams-Watters, May 14 2010
Ambiguous terms a(0), a(1) removed by Max Alekseyev, Jan 18 2012
STATUS
approved