A079063 Least k such that sqrt(prime(n+k))-sqrt(prime(n))>1.

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

Offset

1,1

Comments

Inspired by Andrica's conjecture. If it is true, a(n)>1 for all n.

Cf. A038458, A074976, A078693

Links

Table of n, a(n) for n=1..104.

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....

Prog

(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: A164359 A178307 A327465 * A031352 A374406 A245885

Adjacent sequences: A079060 A079061 A079062 * A079064 A079065 A079066

Keyword

nonn

Author

Benoit Cloitre, Feb 02 2003

Status

approved