id:A094901 - OEIS Search Results

Search: id:A094901

Displaying 1-1 of 1 results found.

page 1

Positive integer values of the integer Schwarzian derivatives of the primes.

+0
1

0, 0, 3, 0, 3, 0, 0, 9, 0, 1, 1, 0, 0, 0, 8, 0, 1, 1, 0, 1, 0, 0, 3, 0, 0, 3, 0, 0, 14, 1, 9, 0, 32, 1, 0, 0, 0, 0, 8, 0, 32, 2, 3, 0, 0, 8, 1, 0, 0, 9, 0, 2, 0, 0, 8, 0, 1, 1, 0, 0, 12, 2, 0, 0, 5, 0, 30, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 29, 0, 32, 1, 1, 0, 0, 3, 0, 0, 0, 1, 1, 0, 3, 0, 0, 45, 0, 10, 1, 2, 0 (list; graph; listen)

	OFFSET	`4,3`
	COMMENT	`Negative values of the integer Schwarzian derivatives of Primes are much larger in magnitude than positives values. The significance of this seems to be in its relationship to zeta zeros on the complex plane.`
	FORMULA	`a(n) = Floor[Abs[IntegerSchwarzianDerivative[Prime[n]]]]`
	MATHEMATICA	`(* Ulam-Newton integer derivatives: ) f1[n_]=Prime[n]-Prime[n-1] f2[n_]=Prime[n]-2Prime[n-1]+Prime[n-2] f3[n_]=Prime[n]-3Prime[n-1]+3Prime[n-2]-Prime[n-3] (* Integer Schwarzian derivative:) sf[n_]=f3[n]/f1[n]-1.5(f2[n]/f1[n])^2 af=Table[sf[n], {n, 4, 204}] a=Floor[Abs[af]]`
	CROSSREFS	`Sequence in context: A126598 A127802 A165951 this_sequence A030220 A055240 A115634` `Adjacent sequences: A094898 A094899 A094900 this_sequence A094902 A094903 A094904`
	KEYWORD	`nonn`
	AUTHOR	`Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 15 2004`

page 1

Search completed in 0.002 seconds

Last modified December 1 13:27 EST 2009. Contains 167806 sequences.

AT&T Labs Research