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A030173
Differences p(i)-p(j) between primes, sorted in numerical order.
15
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
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
KEYWORD
nonn,easy,nice
AUTHOR
Alexander Grasser [Graesser] (alex(AT)computicket.com)
STATUS
approved