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A068314 Smallest integer that can be expressed as the sum of consecutive odd numbers in exactly n ways. 16
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A067536 A139609 A321779 * A152996 A188351 A220443
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

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Last modified February 29 21:35 EST 2024. Contains 370428 sequences. (Running on oeis4.)