OFFSET
1,1
COMMENTS
Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite. - Charles R Greathouse IV, Jun 02 2016
The subsequence of terms where k and k+1 are also squarefree is A318896. - R. J. Mathar, Jul 15 2023
REFERENCES
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Rev. ed. 1997), p. 161 (entry for 7314).
LINKS
Seiichi Manyama, Table of n, a(n) for n = 1..10000
D. A. Goldston, S. W. Graham, J. Pintz and C. Y. Yildirim, Small gaps between almost primes, the parity problem and some conjectures of Erdos on consecutive integers, arXiv:0803.2636 [math.NT], 2008.
FORMULA
MATHEMATICA
a = {}; Do[If[Length[FactorInteger[n]] == 4 && Length[FactorInteger[n + 1]] == 4, AppendTo[a, n]], {n, 1, 100000}]; a (* Artur Jasinski, May 07 2008 *)
Transpose[Position[Partition[PrimeNu[Range[20000]], 2, 1], _?(#[[1]] == #[[2]] == 4&), {1}, Heads->False]][[1]] (* Harvey P. Dale, Jun 21 2013 *)
SequencePosition[PrimeNu[Range[22000]], {4, 4}][[;; , 1]] (* Harvey P. Dale, Jun 20 2024 *)
PROG
(PARI) isok(n) = (omega(n)==4) && (omega(n+1)==4); \\ Michel Marcus, Sep 04 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, May 07 2008
EXTENSIONS
Link provided by Harvey P. Dale, Jun 21 2013
STATUS
approved