The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A264009 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A264009

Table T(i,j) = nonnegative k at which lcm(i+k,j+k) reaches the minimum, read by antidiagonals (i>=1, j>=1).
(history; published version)

#22 by N. J. A. Sloane at Wed Nov 25 02:37:50 EST 2015

STATUS

proposed

approved

#21 by Jon E. Schoenfield at Fri Nov 06 00:45:33 EST 2015

STATUS

editing

proposed

#20 by Jon E. Schoenfield at Fri Nov 06 00:45:31 EST 2015

NAME

Table T(i,j) = nonnegative k at which LCMlcm(i+k,j+k) reaches the minimum, read by antidiagonals (i>=1, j>=1).

EXAMPLE

Let i=10, j=3. Then LCMlcm(i,j)=30, LCMlcm(i+1,j+1)=44, LCMlcm(i+2,j+2)=60, LCMlcm(i+3,j+3)=78, and LCMlcm(i+4,j+4)=14, which is the minimum. Hence T(10,3)=T(3,10)=4.

STATUS

proposed

editing

#19 by Michel Marcus at Sun Nov 01 03:58:28 EST 2015

STATUS

editing

proposed

#18 by Michel Marcus at Sun Nov 01 03:57:53 EST 2015

COMMENTS

T(i,j) = T(j,i).

T(i,j) <= |i-j|.

If i divides j or vice versa, then T(i,j) = 0.

STATUS

proposed

editing

Discussion

Sun Nov 01

03:58

Michel Marcus: Ok

#17 by Ivan Neretin at Sun Nov 01 02:36:58 EST 2015

STATUS

editing

proposed

#16 by Ivan Neretin at Sun Nov 01 02:31:38 EST 2015

CROSSREFS

Cf. A051173A003990.

Discussion

Sun Nov 01

02:36

Ivan Neretin: Surely it could, because symmetry and stuff, but I'd rather leave it the way it is. Pascal triangle, for example, is also symmetric, but is mostly known in the full form, not the half. Also, A003990 seems older than A051173.

#15 by Ivan Neretin at Sun Nov 01 02:29:29 EST 2015

EXAMPLE

Let ni=10, mj=3. Then LCM(n,mi,j)=30, LCM(ni+1,mj+1)=44, LCM(ni+2,mj+2)=60, LCM(ni+3,mj+3)=78, and LCM(ni+4,mj+4)=14, which is the minimum. Hence T(10,3)=T(3,10)=4.

STATUS

proposed

editing

#14 by Michel Marcus at Sun Nov 01 02:08:09 EST 2015

STATUS

editing

proposed

#13 by Michel Marcus at Sun Nov 01 02:06:37 EST 2015

LINKS

<a href="/index/Lc#lcm">Index entries for sequences related to lcm's</a>

CROSSREFS

Cf. A051173.

STATUS

proposed

editing

Discussion

Sun Nov 01

02:08

Michel Marcus: Maybe sequence could be "Triangle read by rows" like A051173 ?