OFFSET
1,2
COMMENTS
Conjectured (Polignac 1849) to be union of even numbers and the odd primes minus 2.
For n > 2: A092953(a(n)) > 0. - Reinhard Zumkeller, Nov 10 2012
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
K. Soundararajan, Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim, Bull. Amer. Math. Soc., 44 (2007), 1-18.
MATHEMATICA
nn = 90; Union[Range[2, nn, 2], Prime[Range[2, PrimePi[nn+2]]] - 2]
PROG
(PARI) print1(1); p=3; forprime(q=5, 1e3, forstep(n=p-1, q-3, 2, print1(", "n)); print1(", ", q-2); p=q) \\ conjectural; Charles R Greathouse IV, Jul 02 2011
(PARI) isOK(n)=if(n%2, isprime(n+2), forprime(p=3, , isprime(n+p)&&return(1)));
for(n=1, 10^100, isOK(n)&print1(n, ", ")) \\ unconditionally outputs correct values only, will "hang" forever if conjecture is false once that exceptional even number is reached; Jeppe Stig Nielsen, Sep 23 2015
(Haskell)
import Data.List.Ordered (union)
a030173 n = a030173_list !! (n-1)
a030173_list = union [2, 4 ..] $ tail a040976_list
-- Reinhard Zumkeller, Jul 03 2015
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
Alexander Grasser [Graesser] (alex(AT)computicket.com)
STATUS
approved