The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A227027 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A227027

Triangular numbers representable as x!/y! with y < x-1.
(history; published version)

#6 by Ralf Stephan at Fri Jul 05 04:49:15 EDT 2013

STATUS

proposed

approved

#5 by Michael B. Porter at Wed Jul 03 12:29:46 EDT 2013

STATUS

editing

proposed

#4 by Michael B. Porter at Sat Jun 29 22:34:57 EDT 2013

NAME

Triangular numbers representable as x!/y! with y < x-1.

EXAMPLE

a(4) 990 is in the sequence since 990 = 11!/8! = 11*10*9 is a ratio of factorials and 990 = (44)(44 + 1)/2 is a triangular number.

STATUS

proposed

editing

#3 by Alex Ratushnyak at Thu Jun 27 21:50:13 EDT 2013

STATUS

editing

proposed

Discussion

Sat Jun 29

22:27

Michael B. Porter: We have room for one more term if it's 37 digits or less.

#2 by Alex Ratushnyak at Thu Jun 27 21:47:54 EDT 2013

NAME

allocated for Alex RatushnyakTriangular numbers representable as x!/y! with y < x-1.

DATA

6, 120, 210, 990, 7140, 185136, 242556, 2162160, 8239770, 258474216, 279909630, 9508687656, 323015470680, 10973017315470, 372759573255306, 12662852473364940, 430164224521152660, 14612920781245825506, 496409142337836914550

OFFSET

1,1

COMMENTS

Triangular numbers in A045619, except A045619(1)=0. The sequence is infinite because A029549 is a subsequence. According to Melissen's comment in A097571, y > x-7.

The sequence of x's producing a(n): A227026.

a(2) and a(3) have two representations:

a(2) = 120 = 5*4*3*2 = 6*5*4.

a(3) = 210 = 7*6*5 = 15*14.

EXAMPLE

a(4) = 11!/8!.

CROSSREFS

Cf. A000217, A001219, A029549, A045619, A097571, A227026.

KEYWORD

allocated

nonn

AUTHOR

Alex Ratushnyak, Jun 27 2013

STATUS

approved

editing

#1 by Alex Ratushnyak at Thu Jun 27 21:47:54 EDT 2013

NAME

allocated for Alex Ratushnyak

KEYWORD

allocated

STATUS

approved