A147813 Primes prime(n) such that (-prime(n) + 2*prime(n+1) - prime(n+2))/((1 - prime(n) + prime(n+1))^(3/2)) < 0.

2, 3, 5, 11, 17, 19, 29, 41, 43, 47, 59, 71, 79, 83, 101, 107, 109, 127, 137, 149, 151, 163, 167, 179, 191, 197, 199, 227, 229, 239, 251, 257, 269, 281, 283, 311, 313, 331, 347, 349, 353, 367, 379, 383, 397, 401, 419, 431, 439, 443, 461, 463, 487, 499, 503, 521

Offset: 1

Author

Roger L. Bagula, Nov 13 2008

Keywords

• nonn

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A036263, A147812 (complement with respect to A000040).

Programs

Haskell

import Data.List (findIndices)
a147813 n = a147813_list !! (n-1)
a147813_list = map (a000040 . (+ 1)) $ findIndices (>= 0) a036263_list
-- Reinhard Zumkeller, Jan 20 2012

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}]]

Formula

Primes prime(n) such that (-prime(n) + 2*prime(n+1) - prime(n+2))/((1 - prime(n) + prime(n+1))^(3/2)) < 0.

Extensions

Edited by Alonso del Arte and Joerg Arndt, Nov 01 2013