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 A079296 Primes ordered by decreasing value of the function p -> sqrt(q) - sqrt(p) where q is the next prime after p. 9
 7, 113, 23, 13, 31, 3, 1327, 19, 47, 199, 139, 89, 5, 211, 293, 53, 523, 317, 61, 181, 73, 887, 1129, 83, 37, 241, 2, 43, 283, 1669, 11, 467, 1069, 337, 509, 2477, 131, 2179, 2971, 1259, 773, 1951, 1637, 409, 3271, 421, 151, 1381, 67, 839, 619, 863, 157, 17, 661, 3137 (list; graph; refs; listen; history; text; internal format)
 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 Cf. A078692, A002386, A084974 (records). Sequence in context: A293456 A099153 A270121 * A081531 A142537 A084974 Adjacent sequences:  A079293 A079294 A079295 * A079297 A079298 A079299 KEYWORD nonn,nice AUTHOR Thomas Nordhaus, Feb 09 2003 EXTENSIONS More terms from Robert G. Wilson v, Oct 18 2012 STATUS approved

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Last modified April 20 02:45 EDT 2021. Contains 343121 sequences. (Running on oeis4.)