OFFSET
1,1
COMMENTS
Goldston, Graham, Pintz & Yıldırım (2005) prove that a(n+1) - a(n) <= 26 infinitely often. They improve this constant to 6 in their 2009 paper. - Charles R Greathouse IV, Dec 26 2020
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
D. A. Goldston, S. W. Graham, J. Pintz and C. Y. Yıldırım, Small gaps between primes and almost primes, arXiv:math/0506067 [math.NT], 2005; Proceedings of the London Mathematical Society 98:3 (May 2009), pp. 741-774.
Yang Liu, Peter S. Park, and Zhuo Qun Song, Bounded gaps between products of distinct primes, arXiv:1607.03887 [math.NT], 2016-2017; Research in Number Theory 3:26 (2017).
Keiju Sono, Small gaps between the set of products of at most two primes, arXiv:1605.02920 [math.NT], 2016-2018; Journal of the Mathematical Society of Japan 72:1 (2020), pp. 81-118.
MATHEMATICA
f[n_]:=Last/@FactorInteger[n]=={1, 1}; a=6; lst={}; Do[If[f[n], AppendTo[lst, n-a]; a=n], {n, 9, 6!}]; lst
PROG
(PARI) {m=106; v=vector(m); n=0; c=0; while(c<m, n++; if(bigomega(n)==2&&omega(n)==2, c++; v[c]=n)); w=vector(m-1, j, v[j+1]-v[j])} \\ Klaus Brockhaus, Oct 13 2009
(Magma) T:=[ n: n in [1..360] | #PrimeDivisors(n) eq 2 and &*[ d[2]: d in Factorization(n) ] eq 1 ]; [ T[j+1]-T[j]: j in [1..#T-1] ]; // Klaus Brockhaus, Oct 13 2009
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Oct 09 2009
EXTENSIONS
Edited by Klaus Brockhaus, Oct 13 2009
Added formula to clarify the definition. - N. J. A. Sloane, Jul 19 2022
STATUS
approved