Perhaps not quite all. 6 & 8 should be swapped. Then the two sequences are 1 2 6 14 35 84 204 ... 1 3 8 20 49 119 288 ... which are A105635 & A048739. Some further comment could be added to each of these. They are closely related to the Bhaskara equation, and are really second order recurrences with a phony root, 1, appended, making them cubic. But it's much more natural to look at A001109 A053141 A001108 A001652 Best to all, R. On Sun, 16 Oct 2005, David Gale wrote:
Neil, Unfortunately I don't have access at the moment to the OEIS, but here is the whole story on the median sequence. I'll be interested to know whether and if so how it qualifies for inclusion.
The integer m in N={1,2,..,n} is a MEDIAN of n if 1+..+m=m+..+n. I write the pair (n,m) . Example: (1,1) is a median pair
The integer m' in N={1,2,..,n} is a SUBMEDIAN of n if 1+..+m'=(m'+1)+..+n. I write the pair (n,m'). Example: (3,2) is a submedian pair. One wants to know which n have medians and submedians. Here are the first 7 pairs, alternately median and submedian.
(1,1) med. (3,2) submed. (6,8) med. (20,14) submed. etc. (49,35) (119,84) (288,204) ...... Here is the fundemental recusion: If (n,m) is a median pair then(n+2m,m+n) is a submedian pair. If (n,m') is a submedian pair them (n+2m'+1,n+m'+1.) is a median pair.
C'est tout.
David
David, is this sequence: For which n does the sequence (1,2, . ,n) have a perfect median? , in the OEIS? If so that property should be noted there, and if not the sequence should be added! Similarly for your other sequence. Can you send me the first few terms? You mentioned a Pellian equation.
Thanks!
Neil
At 08:57 AM 10/6/2005, you wrote:
David, is this sequence: For which n does the sequence (1,2, . ,n) have a perfect median? , in the OEIS? If so that property should be noted there, and if not the sequence should be added! Similarly for your other sequence. Can you send me the first few terms? You mentioned a Pellian equation.
Thanks!
Neil
Neil J. A. Sloane AT&T Shannon Labs, Room C233, 180 Park Avenue, Florham Park, NJ 07932-0971 Email: njas@research.att.com Office: 973 360 8415; fax: 973 360 8178 Home page: http://www.research.att.com/~njas/
math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun