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A006063
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A card-arranging problem: values of n such that there exists a permutation p_1, ..., p_n of 1, ..., n such that i + p_i is a cube for every i.
(Formerly M4361)
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6
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7, 19, 26, 37, 44, 56, 63, 66, 68, 80, 82, 85, 87, 98, 100, 103, 105, 110, 112, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 135, 147, 149, 150, 151, 152, 155, 156, 159, 171, 173, 174, 175, 176, 177, 178, 179
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Apparently Gardner (1975) quotes Papaikonomou as showing that there can be at most one solution for a given n. However, this is incorrect: see A096680 for n values with more than one such permutation. (Ray Chandler)
For any n, the number of permutations is permanent(m), where the n-by-n matrix m is defined m(i,j) = 1 or 0, depending on whether i+j is a cube or not. Hence, n is in this sequence if permanent(m) > 0.
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REFERENCES
| M. Gardner, Mathematical Games column, Scientific American, Mar 1975.
M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 81.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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CROSSREFS
| Cf. A095986 (for squares), A096680.
Sequence in context: A127633 A055246 A003282 * A181123 A038593 A014439
Adjacent sequences: A006060 A006061 A006062 * A006064 A006065 A006066
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| Entry revised Jul 18 2004 based on comments from Franklin T. Adams-Watters.
a(8) and later terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Jul 26 2004
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