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A030173 Differences p(i)-p(j) between primes, sorted in numerical order.

%I A030173 #41 Sep 23 2015 11:09:01
%S A030173 1,2,3,4,5,6,8,9,10,11,12,14,15,16,17,18,20,21,22,24,26,27,28,29,30,
%T A030173 32,34,35,36,38,39,40,41,42,44,45,46,48,50,51,52,54,56,57,58,59,60,62,
%U A030173 64,65,66,68,69,70,71,72,74,76,77,78,80,81,82,84,86,87,88,90
%N A030173 Differences p(i)-p(j) between primes, sorted in numerical order.
%C A030173 Conjectured (Polignac 1849) to be union of even numbers and the odd primes minus 2.
%C A030173 For n > 2: A092953(a(n)) > 0. - _Reinhard Zumkeller_, Nov 10 2012
%H A030173 T. D. Noe, <a href="/A030173/b030173.txt">Table of n, a(n) for n = 1..1000</a>
%H A030173 K. Soundararajan, <a href="http://dx.doi.org/10.1090/S0273-0979-06-01142-6">Small gaps between prime numbers: the work of Goldston-Pintz-Yildirim</a>, Bull. Amer. Math. Soc., 44 (2007), 1-18.
%H A030173 <a href="/index/Pri#gaps">Index entries for primes, gaps between</a>
%t A030173 nn = 90; Union[Range[2, nn, 2], Prime[Range[2, PrimePi[nn+2]]] - 2]
%o A030173 (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
%o A030173 (PARI) isOK(n)=if(n%2,isprime(n+2),forprime(p=3,,isprime(n+p)&&return(1)));
%o A030173 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
%o A030173 (Haskell)
%o A030173 import Data.List.Ordered (union)
%o A030173 a030173 n = a030173_list !! (n-1)
%o A030173 a030173_list = union [2, 4 ..] $ tail a040976_list
%o A030173 -- _Reinhard Zumkeller_, Jul 03 2015
%Y A030173 Complement of A007921. Cf. A001223, A005843, A040976.
%K A030173 nonn,easy,nice
%O A030173 1,2
%A A030173 Alexander Grasser [Graesser] (alex(AT)computicket.com)