The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A004210 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A004210

"Magic" integers: a(n+1) is the smallest integer m such that there is no overlap between the sets {m, m-a(i), m+a(i): 1 <= i <= n} and {a(i), a(i)-a(j), a(i)+a(j): 1 <= j < i <= n}.
(history; published version)

#48 by N. J. A. Sloane at Sun Feb 24 11:21:00 EST 2019

STATUS

editing

approved

#47 by N. J. A. Sloane at Sun Feb 24 11:20:53 EST 2019

REFERENCES

R. A. Bates, E. Riccomagno, R. Schwabe, H. P. Wynn, Lattices and dual lattices in optimal experimental design for Fourier models, Computational Statistics & Data Analysis Volume 28, Issue 3, 4 September 1998, Pages 283-296. See page 293.

STATUS

approved

editing

#46 by N. J. A. Sloane at Sun Oct 08 12:35:55 EDT 2017

STATUS

editing

approved

#45 by N. J. A. Sloane at Sun Oct 08 12:35:26 EDT 2017

LINKS

N. J. A. Sloane, <a href="/A004210/a004210_1.pdf">TITLE FOR LINK</a>

STATUS

approved

editing

Discussion

Sun Oct 08

12:35

N. J. A. Sloane: Deleted a link that did not point anywhere.

#44 by N. J. A. Sloane at Sun Oct 08 12:33:57 EDT 2017

STATUS

proposed

approved

#43 by Jon E. Schoenfield at Sun Oct 08 10:25:59 EDT 2017

STATUS

editing

proposed

#42 by Jon E. Schoenfield at Sun Oct 08 10:25:34 EDT 2017

COMMENTS

The definition implies that the sets {a(i)} (A004210), {a(i)-a(j), j < i} (A206522) and {a(i)+a(j), j < i} (A206523) are disjoint. A206524 gives the complement of their union.

LINKS

T. D. Noe, <a href="/A004210/b004210.txt">Table of n, a(n) for n = 1..150</a>

FORMULA

a(n+1) = min{ k | k and k +/- a(i) are not equal to a(i) or a(i)-a(j) or a(i)+a(j) for any n+1 > i > j > 0}. [Corrected by T. D. Noe, Sep 08 2008]

STATUS

approved

editing

Discussion

Sun Oct 08

10:25

Jon E. Schoenfield: The last Links entry needs a title ... and is located in the wrong place?

#41 by N. J. A. Sloane at Sat Jun 24 22:44:16 EDT 2017

STATUS

editing

approved

#40 by N. J. A. Sloane at Sat Jun 24 22:44:13 EDT 2017

MATHEMATICA

a[1] = 1; a[n_] := a[n] = Module[{pairs = Flatten[ Table[{a[j] + a[k], a[k] - a[j]}, {j, 1, n-1}, {k, j+1, n-1}]], an = a[n-1] + 1}, While[ True, If[ Intersection[ Join[ Array[a, n-1], pairs], Prepend[ Flatten[ Table[{a[j] + an, an - a[j]}, {j, 1, n-1}]], an]] == {}, Break[], an++]]; an]; Table[a[n], {n, 1, 48}] (* Jean-François Alcover, Nov 10 2011 *)

STATUS

approved

editing

#39 by N. J. A. Sloane at Sat Jun 24 22:20:30 EDT 2017

STATUS

editing

approved