

A140078


Numbers k such that k and k+1 have 4 distinct prime factors.


14



7314, 8294, 8645, 9009, 10659, 11570, 11780, 11934, 13299, 13629, 13845, 14420, 15105, 15554, 16554, 16835, 17204, 17390, 17654, 17765, 18095, 18290, 18444, 18920, 19005, 19019, 19095, 19227, 20349, 20405, 20769, 21164, 21489, 21735
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OFFSET

1,1


COMMENTS

Goldston, Graham, Pintz, & Yildirim prove that this sequence is infinite.  Charles R Greathouse IV, Jun 02 2016


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.


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 *)


PROG

(PARI) isok(n) = (omega(n)==4) && (omega(n+1)==4); \\ Michel Marcus, Sep 04 2015


CROSSREFS

Similar sequences with k distinct prime factors: A074851 (k=2), A140077 (k=3), this sequence (k=4), A140079 (k=5).
Cf. A093548.
Equals A321504 \ A321494.
Sequence in context: A206080 A253939 A116248 * A321504 A318896 A295004
Adjacent sequences: A140075 A140076 A140077 * A140079 A140080 A140081


KEYWORD

nonn


AUTHOR

Artur Jasinski, May 07 2008


EXTENSIONS

Link provided by Harvey P. Dale, Jun 21 2013


STATUS

approved



