A075631 - OEIS

A075631

Group the natural numbers so that the n-th group contains smallest set of consecutive numbers whose sum is a multiple of the sum for the previous group: (1), (2), (3, 4, 5), (6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18), (19, 20, ... Sequence gives sums of terms of the groups.

1, 2, 12, 156, 4680, 42120, 43931160, 1489793497920, 89075729055377937600, 51745303414377493336016875691726400, 11120662689162548692119420650118842670724939176955384978536000

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Let n be the last term of a group with sum s. The end of the next group is computed by solving x^2 + x - n*(n+1) == 0 (mod 2*s) and picking the smallest solution x > n. For example to find the term after 12 (the (3,4,5) group), solve x^2 + x - 5*6 == 0 (mod 2*12). The solutions are x = {2, 5, 18, 24}; the end of the next group must be 18 and so the next term is Sum_{i=6..18} i = 156. - Jonathan Cross (jcross(AT)juggler.net), May 08 2004

LINKS

Table of n, a(n) for n=1..11.

CROSSREFS

Cf. A075632, A075633, A075634, A079798.

Sequence in context: A365863 A366203 A130529 * A127182 A330552 A326222

Adjacent sequences: A075628 A075629 A075630 * A075632 A075633 A075634

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 30 2002

EXTENSIONS

More terms from Jonathan Cross (jcross(AT)juggler.net), May 08 2004

STATUS

approved