OFFSET
1,1
COMMENTS
For each consecutive prime pair p < q, d = sqrt(q) - sqrt(p) is unique. Place d in order from greatest to least and specify p.
Last appearance by prime index: 1, 5, 7, 10, 13, 17, 20, 26, 28, 33, 35, 41, 43, 45, 49, ..., .
Last appearance of a minimum prime by Andrica ranking: 2, 11, 17, 29, 41, 59, 71, 101, 107, 137, 149, 179, ..., .
As expected, this sequence is the lesser of the twin primes beginning with the second term, 11. See A001359.
LINKS
Marek Wolf, A Note on the Andrica Conjecture, arXiv:1010.3945 [math.NT], 2010.
EXAMPLE
MATHEMATICA
lst = {}; p = 2; q = 3; While[p < 1600000, If[ Sqrt[q] - Sqrt[p] > 1/20, AppendTo[lst, {p, Sqrt[q] - Sqrt[p]}]]; p = q; q = NextPrime[q]]; lsu = First@ Transpose@ Sort[lst, #1[[2]] > #2[[2]] &]; Table[ Position[lsu, p, 1, 1], {p, Prime@ Range@ 65}] // Flatten
CROSSREFS
KEYWORD
nonn
AUTHOR
Marek Wolf and Robert G. Wilson v, Oct 18 2012
STATUS
approved