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Search: id:A004210
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| A004210 |
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"Magic" integers: a(n+1) is the smallest integer so that neither itself, nor sum or difference with earlier a(i) is already contained in the set of pairwise differences or pairwise sums or a(i) itself.
(Formerly M2728)
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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This implies that the union of the sequence together with all pairwise sums and products form a unique set without multiplicities.
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
D. R. Hofstadter, "Goedel, Escher, Bach: An Eternal Golden Braid", Basic Books Incorparated,pg. 73
P. Mark Kayll, Well-spread sequences and edge-labelings with constant Hamiltonian weight, Disc. Math. & Theor. Comp. Sci 6 2 (2004) 401-408
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..150
J. V. Silverton, On the generation of 'magic integrals', Acta Cryst. A34 (1978) p 634.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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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]
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CROSSREFS
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Cf. A000969 A005228.
Sequence in context: A101822 A088589 A063597 this_sequence A119881 A075342 A083726
Adjacent sequences: A004207 A004208 A004209 this_sequence A004211 A004212 A004213
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KEYWORD
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easy,nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Additional comments from Robert M. Burton, Jr. (bob(AT)oregonstate.edu), Feb 20 2005
More terms from Joshua Zucker (joshua.zucker(AT)stanfordalumni.org), May 04 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Sep 06 2008 at the suggestion of R. J. Mathar
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