A068314 Smallest integer that can be expressed as the sum of consecutive odd numbers in exactly n ways.

1, 9, 45, 96, 144, 240, 768, 480, 720, 960, 2304, 1440, 5184, 3600, 2880, 3360, 36864, 5040, 3145728, 6720, 11520, 61440, 14400, 10080, 25920, 245760, 25200, 26880, 9437184, 20160, 12884901888, 30240, 184320, 3932160, 103680, 40320

Offset

1,2

Comments

The sequence continues: ?,30240,184320,3932160,103680,40320,?,129600,737280,60480,176400,80640,?,430080,100800 where ? is a value > 20000000. A value always exists since 3*(2^(i+1)) is an upper bound for the i-th term (i odd) and 5*3*(2^((i+2)/2)) is an upper bound for i even. Based on these limits, the bounds on the 31st, 37th and 43rd terms are 12884901888, 824633720832 and 52776558133248 respectively. - Larry Reeves (larryr(AT)acm.org), Dec 18 2002

Also the smallest integer that can be expressed as a difference of squares in exactly n ways. - J. M. Bergot, May 09 2019

Links

Don Reble, Table of n, a(n) for n = 1..2000

Example

45 = 45 = 13+15+17 = 5+7+9+11+13, 45 is the smallest number expressible in 3 ways, so a(3)=45.

Crossrefs

Cf. A038548, A034178, A001227.

Sequence in context: A067536 A139609 A321779 * A152996 A188351 A220443

Adjacent sequences: A068311 A068312 A068313 * A068315 A068316 A068317

Keyword

nonn

Author

Naohiro Nomoto, Feb 26 2002

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Dec 18 2002

Further terms from Don Reble, Sep 08 2006

Status

approved