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A140079
Numbers n such that n and n+1 have 5 distinct prime factors.
13
254540, 310155, 378014, 421134, 432795, 483405, 486590, 486794, 488565, 489345, 507129, 522444, 545258, 549185, 558789, 558830, 567644, 577940, 584154, 591260, 598689, 627095, 634809, 637329, 663585, 666995, 667029, 678755, 687939, 690234
OFFSET
1,1
COMMENTS
For the smallest number r such that r and r+1 have n distinct prime factors, see A093548.
Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite. - Charles R Greathouse IV, Jun 02 2016
Subsequence of the variant A321505 defined with "at least 5" instead of "exactly 5" distinct prime factors. See A321495 for the differences. - M. F. Hasler, Nov 12 2018
The subset of numbers where n and n+1 are also squarefree gives A318964. - R. J. Mathar, Jul 15 2023
LINKS
D. A. Goldston, S. W. Graham, J. Pintz, 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
{k: k in A051270 and k+1 in A051270}. - R. J. Mathar, Jul 19 2023
MATHEMATICA
a = {}; Do[If[Length[FactorInteger[n]] == 5 && Length[FactorInteger[n + 1]] == 5, AppendTo[a, n]], {n, 1, 100000}]; a (*Artur Jasinski*)
Transpose[SequencePosition[Table[If[PrimeNu[n]==5, 1, 0], {n, 700000}], {1, 1}]][[1]] (* The program uses the SequencePosition function from Mathematica version 10 *) (* Harvey P. Dale, Jul 25 2015 *)
PROG
(PARI) is(n)=omega(n)==5 && omega(n+1)==5 \\ Charles R Greathouse IV, Jun 02 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Artur Jasinski, May 07 2008
STATUS
approved