A055095 - OEIS

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A055095

a(n) = 2*A000120[A003188[A055094[n]]] - (n-1) = 2*A005811[A055094[n]] - (n-1).

0, 1, 2, 1, 2, 3, 2, 1, 4, 1, 2, 1, 2, 3, 2, -3, 2, 7, 2, -3, 4, 3, 2, -3, 14, 1, 10, -3, 2, 3, 2, -11, 4, 1, -2, -7, 2, 3, 2, -11, 2, 7, 2, -7, -4, 3, 2, -19, 8, 25, 2, -11, 2, 19, -6, -15, 4, 1, 2, -19, 2, 3, -6, -23, -10, 7, 2, -15, 4, -5, 2, -27, 2, 1, 6, -15, -4, 3, 2, -39, 28, 1, 2, -27, -14, 3, 2, -27, 2, -9, -10, -19, 4, 3, -14, -47, 2, 15, -14, -19, 2, 3, 2, -35, -24 (list; graph; refs; listen; history; internal format)

	OFFSET	`1,3`
	COMMENTS	`For all odd primes p, a(p) = +2 because Sum_{a=1..(p-2)} L((a(a+1))/p) = Sum_{a=1..(p-2)} L((1+(a^-1))/p) = -1; i.e. in Gray code expansion of A055094[p], the number of 1-bits is number of 0-bits + 2. However, a(n) = +2 also for some nonprime odd n = A055131.`
	REFERENCES	`See problem 9.2.2 in Elementary Number Theory by David M. Burton, ISBN 0-205-06978-9`
	FORMULA	`a(n) = (2*wt(GrayCode(qrs2bincode(n))))-(n-1)`
	MAPLE	`GrayCode := n -> XORnos(n, floor(n/2)); # wt (number of 1-bits in binary expansion) given in A000120.`
	CROSSREFS	`Sequence in context: A133088 A059982 A134388 * A048685 A101050 A128979` `Adjacent sequences: A055092 A055093 A055094 * A055096 A055097 A055098`
	KEYWORD	`sign`
	AUTHOR	`Antti Karttunen Apr 04 2000`

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Last modified February 14 23:53 EST 2012. Contains 205689 sequences.