OFFSET
1,1
COMMENTS
I computed a couple of thousand primes with EXCEL and ordered them accordingly. There is a very small chance that very large prime numbers will change the order of the given terms above.
This sequence only makes sense if the sequence n -> sqrt(p_(n+1)) - sqrt(p_n) is a zero-sequence which is a hard unsolved problem. See also Andrica's conjecture.
For each consecutive prime pair p < q, the number d = sqrt(q) - sqrt(p) is unique. Place d in order from greatest to least and specify p. See Table II in Wolf. A rearrangement of the primes. - Robert G. Wilson v, Oct 18 2012
LINKS
Donovan Johnson, Table of n, a(n) for n = 1..10000
C. K. Caldwell, Gaps between primes.
Eric W. Weisstein, Andrica's Conjecture
Wikipedia, Andrica's conjecture
Marek Wolf, A note on the Andrica conjecture, arXiv:1010.3945 [math.NT], 2010.
MATHEMATICA
lim = 1/5; lst = {}; p = 2; q = 3; While[p < 50000, If[ Sqrt[q] - Sqrt[p] > lim, AppendTo[lst, {p, Sqrt[q] - Sqrt[p]}]]; p = q; q = NextPrime[q]]; First@ Transpose@ Sort[lst, #1[[2]] > #2[[2]] &] (* Robert G. Wilson v, Oct 18 2012 *)
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Thomas Nordhaus, Feb 09 2003
EXTENSIONS
More terms from Robert G. Wilson v, Oct 18 2012
STATUS
approved