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

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, 32, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 48, 50, 51, 52, 54, 56, 57, 58, 59, 60, 62, 64, 65, 66, 68, 69, 70, 71, 72, 74, 76, 77, 78, 80, 81, 82, 84, 86, 87, 88, 90

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.

Index entries for primes, gaps between

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

Complement of A007921. Cf. A001223, A005843, A040976.

Sequence in context: A184520 A047248 A114024 * A048265 A288712 A002180

Adjacent sequences: A030170 A030171 A030172 * A030174 A030175 A030176

Keyword

nonn,easy,nice

Author

Alexander Grasser [Graesser] (alex(AT)computicket.com)

Status

approved