cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A206524 By definition, the sequences A004210, A206522 and A206523 are disjoint; the present sequence gives the complement of their union.

Original entry on oeis.org

6, 14, 16, 36, 50, 53, 54, 56, 57, 63, 65, 74, 77, 78, 81, 84, 86, 88, 95, 96, 101, 102, 107, 109, 113, 115, 116, 127, 132, 134, 136, 137, 141, 142, 148, 150, 151, 154, 155, 163, 166, 168, 173, 177, 180, 181, 182, 185, 188, 192, 196, 197, 200, 207, 209, 213, 216, 218, 221, 222, 223, 224, 225, 226, 229, 231, 234, 237, 239, 240, 241, 243, 244, 247, 254
Offset: 1

Views

Author

N. J. A. Sloane, Feb 08 2012

Keywords

Crossrefs

Cf. A004210, A206522, A206524.

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}.

Original entry on oeis.org

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
Offset: 1

Views

Author

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

Keywords

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

  • 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.
  • 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

Crossrefs

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

Programs

  • 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
  • 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 *)

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]

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

A206522 The pairwise differences of the terms of A004210.

Original entry on oeis.org

2, 5, 7, 10, 12, 13, 15, 17, 20, 22, 23, 24, 25, 27, 28, 29, 32, 34, 35, 37, 39, 40, 41, 42, 45, 47, 49, 52, 55, 58, 59, 60, 62, 64, 66, 69, 71, 72, 76, 79, 80, 82, 83, 87, 89, 92, 94, 99, 100, 103, 104, 105, 106, 111, 112, 114, 117, 118, 119, 121, 124, 126, 128, 129, 131, 135, 138, 139, 143, 144, 145, 146, 147, 149, 153, 156, 158, 159, 160, 167, 170, 171, 172, 174, 175
Offset: 1

Views

Author

N. J. A. Sloane, Feb 08 2012

Keywords

Crossrefs

Cf. A004210, A206523, A206524.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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