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A079063
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Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1.
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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; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Inspired by Andrica's conjecture. If it is true, a(n)>1 for all n.
Cf. A038458, A074976, A078693
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LINKS
| Eric Weisstein's World of Mathematics, Andrica's conjecture
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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....
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PROG
| (PARI) a(n)=if(n<0, 0, k=1; while(abs(sqrt(prime(n+k))-sqrt(prime(n)))<1, k++); k)
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CROSSREFS
| Sequence in context: A076662 A164359 A178307 * A031352 A188834 A057853
Adjacent sequences: A079060 A079061 A079062 * A079064 A079065 A079066
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KEYWORD
| nonn
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AUTHOR
| Benoit Cloitre (benoit7848c(AT)orange.fr), Feb 02 2003
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