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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}.
(Formerly M2728)
5
1, 3, 8, 18, 30, 43, 67, 90, 122, 161, 202, 260, 305, 388, 416, 450, 555, 624, 730, 750, 983, 1059, 1159, 1330, 1528, 1645, 1774, 1921, 2140, 2289, 2580, 2632, 2881, 3158, 3304, 3510, 3745, 4086, 4563, 4741, 4928, 5052, 5407, 5864, 6242, 6528, 6739, 7253 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

REFERENCES

D. R. Hofstadter, "Goedel, Escher, Bach: An Eternal Golden Braid", Basic Books Incorporated, p. 73

P. Mark Kayll, Well-spread sequences and edge-labelings with constant Hamiltonian weight, Disc. Math. & Theor. Comp. Sci 6 2 (2004) 401-408

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 1..150

B. G. DeBoer, Letter to N. J. A. Sloane, Dec 15 1978, with enclosure of Silvertom article.

J. V. Silverton, On the generation of 'magic integrals', Acta Cryst. A34 (1978) p. 634.

Eric Weisstein's World of Mathematics, Magic Integer.

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]

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-Fran├žois Alcover, Nov 10 2011 *)

PROG

(Haskell)

import Data.List (intersect)

a004210 n = a004210_list !! (n-1)

a004210_list = magics 1 [0] [0] where

   magics :: Integer -> [Integer] -> [Integer] -> [Integer]

   magics n ms tests

      | tests `intersect` nMinus == [] && tests `intersect` nPlus == []

      = n : magics (n+1) (n:ms) (nMinus ++ nPlus ++ tests)

      | otherwise

      = magics (n+1) ms tests

      where nMinus = map (n -) ms

            nPlus  = map (n +) ms

-- magics works also as generator for a126428_list, cf. A126428.

-- Reinhard Zumkeller, Mar 03 2011

CROSSREFS

Cf. A000969, A005228, A206522, A206523, A206524.

Sequence in context: A063597 A171701 A288249 * A247022 A119881 A184636

Adjacent sequences:  A004207 A004208 A004209 * A004211 A004212 A004213

KEYWORD

easy,nonn,nice

AUTHOR

N. J. A. Sloane, following a suggestion from B. G. DeBoer, Dec 15 1978

EXTENSIONS

Additional comments from Robert M. Burton, Jr. (bob(AT)oregonstate.edu), Feb 20 2005

More terms from Joshua Zucker, May 04 2006

Edited by N. J. A. Sloane, Sep 06 2008 at the suggestion of R. J. Mathar

Edited by N. J. A. Sloane, Feb 08 2012

STATUS

approved

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Last modified January 15 18:43 EST 2019. Contains 319159 sequences. (Running on oeis4.)