id:A091569 - OEIS Search Results

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a(1) = 1; for n > 1, a(n) is the smallest positive integer not already used such that a(n)*a(n-1) + 1 is a perfect square.

+0
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1, 3, 5, 7, 9, 11, 13, 15, 8, 6, 4, 2, 12, 10, 36, 34, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 52, 50, 48, 35, 33, 31, 29, 27, 25, 23, 21, 19, 17, 64, 62, 60, 40, 38, 148, 146, 144, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`Does this sequence contain every positive integer? We could get an equally interesting sequence by choosing a(1) to be any other positive integer.`
	EXAMPLE	`10 is followed by 36 because 10*36+1 = 19^2 and 8 and 12 were already used.`
	PROGRAM	`(Matlab) program by D. Wasserman A = zeros(1, 100); A(1) = 1; used = zeros(1, 1000); used(1) = 1; for i = 2:100; found = 0; k = 0; while found == 0; k = k + 1; if used(k) == 0; s = sqrt(k*A(i - 1) + 1); if s == floor(s); A(i) = k; used(k) = 1; found = 1; end; end; end; end; A`
	CROSSREFS	`Cf. A083203.` `Sequence in context: A007617 A065878 A064996 this_sequence A120890 A134322 A063460` `Adjacent sequences: A091566 A091567 A091568 this_sequence A091570 A091571 A091572`
	KEYWORD	`easy,nonn`
	AUTHOR	`David Wasserman (wasserma(AT)spawar.navy.mil), Mar 04 2004`

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Last modified December 7 23:50 EST 2009. Contains 170430 sequences.

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