login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A006049 Numbers n such that n and n+1 have same number of distinct prime divisors. 9
2, 3, 4, 7, 8, 14, 16, 20, 21, 31, 33, 34, 35, 38, 39, 44, 45, 50, 51, 54, 55, 56, 57, 62, 68, 74, 75, 76, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 111, 115, 116, 117, 118, 122, 123, 127, 133, 134, 135, 141, 142, 143, 144, 145, 146, 147, 152, 158, 159, 160, 161, 171, 175 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Sequence is infinite, as proved by Schlage-Puchta who comments: "Buttkewitz found a non-computational proof, and the Goldston-Pintz-Yildirim-sieve yields more precise information". - Charles R Greathouse IV, Jan 09 2013

REFERENCES

C. Clawson, Mathematical mysteries, Plenum Press 1996, p. 250.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..2500

Jan-Christoph Schlage-Puchta, The equation ω(n)=ω(n+1), 2011

FORMULA

A001221(a(n)) = A001221(a(n)+1). - Reinhard Zumkeller, Jan 22 2013

MATHEMATICA

f[n_] := Length@FactorInteger[n]; t = f /@ Range[175]; Flatten@Position[Rest[t] - Most[t], 0] (* Ray Chandler *)

Select[Range[200], PrimeNu[#]==PrimeNu[#+1]&] (* Harvey P. Dale, May 09 2012 *)

Flatten[Position[Partition[PrimeNu[Range[200]], 2, 1], _?(#[[1]]==#[[2]]&), {1}, Heads->False]] (* Harvey P. Dale, May 22 2015 *)

PROG

(PARI) is(n)=omega(n)==omega(n+1) \\ Charles R Greathouse IV, Jan 09 2013

(Haskell)

import Data.List (elemIndices)

a006049 n = a006049_list !! (n-1)

a006049_list = map (+ 1) $ elemIndices 0 $

   zipWith (-) (tail a001221_list) a001221_list

-- Reinhard Zumkeller, Jan 22 2013

CROSSREFS

Cf. A001221, A052215, A107800, A006073.

Subsequence of A062974.

Sequence in context: A057887 A202116 A215914 * A084541 A240690 A113050

Adjacent sequences:  A006046 A006047 A006048 * A006050 A006051 A006052

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane.

EXTENSIONS

Extended by Ray Chandler, Mar 27 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.