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A163263 Numbers having multiple representations as the product of non-overlapping ranges of consecutive numbers. 2
210, 720, 175560, 17297280 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 21 11:01 EST 2018. Contains 317447 sequences. (Running on oeis4.)