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

Author

Naohiro Nomoto, Feb 26 2002

Keywords

• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A038548, A034178, A001227.

Extensions

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

Further terms from Don Reble, Sep 08 2006