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 A147812 Primes prime(n) such that prime(n+1) - prime(n) > prime(n+2) - prime(n+1). 6
 7, 13, 23, 31, 37, 53, 61, 67, 73, 89, 97, 103, 113, 131, 139, 157, 173, 181, 193, 211, 223, 233, 241, 263, 271, 277, 293, 307, 317, 337, 359, 373, 389, 409, 421, 433, 449, 457, 467, 479, 491, 509, 523 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS This was originally formulated as (-prime(n) + 2*prime(n+1) - prime(n+2))/((1 - prime(n) + prime(n+1))^(3/2)) > 0, which relates it to other sequences. This is equivalent since the denominator is always positive. LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 EXAMPLE The gap between 7 and the next prime, 11, is 4, which is greater than the next prime gap from 11 to 13, so 7 is in the sequence. MATHEMATICA d2[n_] = Prime[n + 2] - 2*Prime[n + 1] + Prime[n]; d1[n_] = Prime[n + 1] - Prime[n]; k[n_] = -d2[n]/(1 + d1[n])^(3/2); Flatten[Table[If[k[n] > 0, Prime[n], {}], {n, 1, 100}]] PROG (Haskell) import Data.List (findIndices) a147812 n = a147812_list !! (n-1) a147812_list = map (a000040 . (+ 1)) \$ findIndices (< 0) a036263_list -- Reinhard Zumkeller, Jan 20 2012 (Ruby) require 'mathn' Prime.take(100).each_cons(3).select{ |a, b, c| b-a>c-b }.map(&:first) -- Aaron Weiner, Dec 05 2013 CROSSREFS Cf. A036263, A147813 (complement with respect to A000040). Sequence in context: A106349 A293657 A048449 * A043884 A129727 A275897 Adjacent sequences:  A147809 A147810 A147811 * A147813 A147814 A147815 KEYWORD nonn AUTHOR Roger L. Bagula, Nov 13 2008 EXTENSIONS Edited by Alonso del Arte and Joerg Arndt, Nov 01 2013 Simpler formula added by Aaron Weiner, Dec 05 2013 STATUS approved

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Last modified April 23 22:41 EDT 2019. Contains 322389 sequences. (Running on oeis4.)