cp's OEIS Frontend

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.

%I A006063 M4361 #19 Aug 28 2018 10:46:04
%S A006063 7,19,26,37,44,56,63,66,68,80,82,85,87,98,100,103,105,110,112,115,116,
%T A006063 117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,
%U A006063 135,147,149,150,151,152,155,156,159,171,173,174,175,176,177,178,179
%N 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.
%C A006063 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_
%C A006063 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.
%D A006063 M. Gardner, Mathematical Games column, Scientific American, Mar 1975.
%D A006063 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, NY, 1988, p. 81.
%D A006063 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%F A006063 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
%Y A006063 Cf. A095986 (for squares), A096680.
%K A006063 nonn
%O A006063 1,1
%A A006063 _N. J. A. Sloane_
%E A006063 Entry revised Jul 18 2004 based on comments from _Franklin T. Adams-Watters_
%E A006063 a(8) and later terms from _Ray Chandler_, Jul 26 2004