|
| |
|
|
A051634
|
|
Strong primes: prime(n) > (prime(n-1) + prime(n+1))/2.
|
|
30
|
|
|
|
11, 17, 29, 37, 41, 59, 67, 71, 79, 97, 101, 107, 127, 137, 149, 163, 179, 191, 197, 223, 227, 239, 251, 269, 277, 281, 307, 311, 331, 347, 367, 379, 397, 419, 431, 439, 457, 461, 479, 487, 499, 521, 541, 557, 569, 587, 599
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Prime(n) such that prime(n)-prime(n-1) > prime(n+1)-prime(n) [from Juri-Stepan Gerasimov, Jan 01 2011).
a(n) > A051635(n). [Thomas Ordowski, Jul 25 2012]
|
|
|
REFERENCES
|
A. Murthy, Smarandache Notions Journal, Vol. 11 N. 1-2-3 Spring 2000
|
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n = 1..1000
|
|
|
EXAMPLE
|
11 belongs to the sequence because 11>(7+13)/2
|
|
|
MATHEMATICA
|
Transpose[Select[Partition[Prime[Range[10^2]], 3, 1], #[[2]]>(#[[1]]+#[[3]])/2 &]][[2]] (from Vladimir Joseph Stephan Orlovsky, May 01 2008)
p=Prime[Range[200]]; p[[Flatten[1+Position[Sign[Differences[p, 2]], -1]]]]
|
|
|
PROG
|
(PARI) p=2; q=3; forprime(r=5, 1e4, if(2*q>p+r, print1(q", ")); p=q; q=r) \\ Charles R Greathouse IV, Jul 19 2011
(Haskell)
a051634 n = a051634_list !! (n-1)
a051634_list = f a000040_list where
f (p:qs@(q:r:ps)) = if 2 * q > (p + r) then q : f qs else f qs
-- Reinhard Zumkeller, May 09 2013
|
|
|
CROSSREFS
|
Cf. A006562, A051635.
Subsequence of A178943; A225493 (multiplicative closure).
Sequence in context: A110055 A105886 A225493 * A038918 A220293 A166307
Adjacent sequences: A051631 A051632 A051633 * A051635 A051636 A051637
|
|
|
KEYWORD
|
nice,nonn,changed
|
|
|
AUTHOR
|
Felice Russo, Nov 15 1999
|
|
|
STATUS
|
approved
|
| |
|
|
