id:A079063 - OEIS Search Results

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Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1.

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3, 3, 2, 3, 3, 3, 3, 2, 3, 3, 4, 4, 4, 3, 4, 4, 5, 4, 5, 4, 4, 4, 4, 5, 6, 5, 4, 4, 3, 3, 5, 5, 5, 5, 6, 5, 6, 5, 6, 7, 6, 5, 5, 4, 4, 4, 7, 7, 7, 6, 6, 6, 6, 8, 7, 7, 6, 5, 6, 6, 6, 5, 6, 6, 6, 6, 7, 7, 8, 7, 7, 7, 7, 7, 6, 7, 6, 7, 7, 8, 8, 9, 9, 8, 8, 7, 8, 8, 8, 7, 7, 8, 7, 6, 6, 6, 5, 6, 6, 8, 8, 9, 9, 10 (list; graph; listen)

	OFFSET	`1,1`
	COMMENT	`Inspired by Andrica's conjecture. If it is true, a(n)>1 for all n.` `Cf. A038458, A074976, A078693`
	LINKS	`Eric Weisstein's World of Mathematics, Andrica's conjecture`
	FORMULA	`Conjecture: there is a constant c>0 such that for n large enough, a(n)>c*sqrt(n) and we can take c=0.4. More precisely, there are 2 constants A and B such that A=lim sup n ->infinity a(n)/sqrt(n) exists = 0.75....; B=lim inf n ->infinity a(n)/sqrt(n) exists =0.46....`
	PROGRAM	`(PARI) a(n)=if(n<0, 0, k=1; while(abs(sqrt(prime(n+k))-sqrt(prime(n)))<1, k++); k)`
	CROSSREFS	`Sequence in context: A060586 A076662 A164359 this_sequence A031352 A057853 A129309` `Adjacent sequences: A079060 A079061 A079062 this_sequence A079064 A079065 A079066`
	KEYWORD	`nonn`
	AUTHOR	`Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003`

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Last modified December 9 14:43 EST 2009. Contains 170430 sequences.

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