

A163263


Numbers having multiple representations as the product of nonoverlapping ranges of consecutive numbers.


2




OFFSET

1,1


COMMENTS

A subsequence of A064224. This sequence gives solutions P to the equation P = (x+1)...(x+m) = (y+1)...(y+n) with x>0, y>0 and x+m < y+1. So far, no numbers P with more than two representations have been discovered. Note that the only the lowest range of consecutive numbers (x+1 to x+m) can contain prime numbers; the other ranges are in a gap between consecutive primes. Gaps between the first 45000 primes were searched for additional terms, but none were found.


LINKS

Table of n, a(n) for n=1..4.
Carlos Rivera, Puzzle 469


EXAMPLE

210 = 5*6*7 = 14*15.
720 = 2*3*4*5*6 = 8*9*10.
175560 = 19*20*21*22 = 55*56*57.
17297280 = 8*9*10*11*12*13*14 = 63*64*65*66.


CROSSREFS

Sequence in context: A235921 A236432 A118279 * A009127 A158559 A235248
Adjacent sequences: A163260 A163261 A163262 * A163264 A163265 A163266


KEYWORD

nonn


AUTHOR

T. D. Noe, Jul 29 2009


STATUS

approved



