A071984 - OEIS

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A071984

Square loops: the number of circular permutations (reversals not counted as different) of the numbers 1 to n such that the sum of any two consecutive numbers is a square.

1, 1, 11, 57, 31, 20, 25, 50, 64, 464, 1062, 4337, 10091, 21931, 69623, 115913, 227893, 457707 (list; graph; refs; listen; history; internal format)

	OFFSET	`32,3`
	COMMENTS	`It is unknown whether a circular permutation of the numbers 1 to n exists such that the sum of any two consecutive numbers is a cube.` `According to Rivera's Puzzle 311, the smallest n for which a cubic loop exists is 473. - T. D. Noe (noe(AT)sspectra.com), Nov 26 2007`
	LINKS	`Carlos Rivera, Puzzle 311: Sum to a cube`
	EXAMPLE	`There is only one possible square loop of minimum length, which is: (32, 4, 21, 28, 8, 1, 15, 10, 26, 23, 2, 14, 22, 27, 9, 16, 20, 29, 7, 18, 31, 5, 11, 25, 24, 12, 13, 3, 6, 30, 19, 17) so a(32)=1.`
	CROSSREFS	`Cf. A071983, A112663.` `Sequence in context: A051946 A201150 A114030 * A101094 A187693 A200529` `Adjacent sequences: A071981 A071982 A071983 * A071985 A071986 A071987`
	KEYWORD	`nice,nonn`
	AUTHOR	`William Rex Marshall (w.r.marshall(AT)actrix.co.nz), Jun 16 2002`
	EXTENSIONS	`a(48)-a(49) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Sep 14 2010`

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Last modified February 12 07:16 EST 2012. Contains 205370 sequences.