A006063 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)

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

Offset

1,1

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 X 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.

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).

Links

Table of n, a(n) for n=1..55.

Formula

Conjecture: a(n) = n + 124 for n >= 173, i.e. there is such a permutation for every n >= 173. Verified for 173 <= n <= 1000. - Robert Israel, Aug 28 2018

Crossrefs

Cf. A095986 (for squares), A096680.

Sequence in context: A127633 A055246 A003282 * A181123 A038593 A014439

Adjacent sequences: A006060 A006061 A006062 * A006064 A006065 A006066

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Entry revised Jul 18 2004 based on comments from Franklin T. Adams-Watters

a(8) and later terms from Ray Chandler, Jul 26 2004

Status

approved