login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A225837 Numbers of form 2^i*3^j*(6k+1), i, j, k >= 0. 6

%I #33 Feb 10 2024 02:19:50

%S 1,2,3,4,6,7,8,9,12,13,14,16,18,19,21,24,25,26,27,28,31,32,36,37,38,

%T 39,42,43,48,49,50,52,54,55,56,57,61,62,63,64,67,72,73,74,75,76,78,79,

%U 81,84,85,86,91,93,96,97,98,100,103,104,108,109,110,111,112

%N Numbers of form 2^i*3^j*(6k+1), i, j, k >= 0.

%C The asymptotic density of this sequence is 1/2. - _Amiram Eldar_, Apr 03 2022

%C From _Peter Munn_, Nov 16 2023: (Start)

%C Contains all nonzero squares.

%C Dividing by 5 the terms that are multiples of 5 gives its complement, A225838.

%C (A352272, 2*A352272, 3*A352272, 6*A352272) is a partition of the terms.

%C The terms form a subgroup of the positive integers under the operation A059897(.,.) and are the positive integers in an index 2 multiplicative subgroup of rationals that is generated by 2, 3 and integers congruent to 1 modulo 6. See A225857 and A352272 for further information about such subgroups.

%C (End)

%H Amiram Eldar, <a href="/A225837/b225837.txt">Table of n, a(n) for n = 1..10000</a>

%t mx = 122; t = {}; Do[n = 2^i*3^j (6 k + 1); If[n <= mx, AppendTo[t, n]], {i, 0, Log[2, mx]}, {j, 0, Log[3, mx]}, {k, 0, mx/6}]; Union[t] (* _T. D. Noe_, May 16 2013 *)

%o (PARI) for(n=1,200,t=n/(2^valuation(n,2)*3^valuation(n,3));if((t%6==1),print1(n,",")))

%o (Magma) [n: n in [1..200] | IsOne(d mod 6) where d is n div (2^Valuation(n,2)*3^Valuation(n,3))]; // _Bruno Berselli_, May 16 2013

%Y Complement of A225838.

%Y Subsequences: A003136\{0}, A083854\{0}, A260488\{0}, A352272.

%Y Symmetric difference of A026225 and A036554; of A036668 and A189716.

%Y Cf. A016921, A059897, A225857.

%K nonn,easy

%O 1,2

%A _Ralf Stephan_, May 16 2013

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)