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!)
A135765 Distribute the odd numbers in columns based on the occurrence of "3" in each prime factorization; square array A(row, col) = 3^(row-1) * A007310(col), read by antidiagonals A(1,1), A(1,2), A(2,1), A(1,3), A(2,2), A(3,1), ... 10
1, 5, 3, 7, 15, 9, 11, 21, 45, 27, 13, 33, 63, 135, 81, 17, 39, 99, 189, 405, 243, 19, 51, 117, 297, 567, 1215, 729, 23, 57, 153, 351, 891, 1701, 3645, 2187, 25, 69, 171, 459, 1053, 2673, 5103, 10935, 6561, 29, 75, 207, 513, 1377, 3159, 8019, 15309, 32805 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The Table can be constructed by multiplying sequence A000244 by A007310.
From Antti Karttunen, Jan 26 2015: (Start)
A permutation of odd numbers. Adding one to each term and then dividing by two gives a related table A254051, which for any odd number, located in this array as x = A(row,col), gives the result at A254051(row+1,col) after one combined Collatz step (3x+1)/2 -> x (A165355) has been applied.
Each odd number n occurs here in position A(A007949(n), A126760(n)).
Compare also to A135764.
(End)
LINKS
FORMULA
From Antti Karttunen, Jan 26 2015: (Start)
With both row and col starting from 1:
A(row, col) = A000244(row-1) * A007310(col) = 3^(row-1) * A007310(col).
a(n) = (2*A254051(n))-1.
a(n) = A003961(A254053(n)).
Above in array form:
A(row,col) = A003961(A254053(row,col)) = A003961(A135764(row,A249745(col))).
(End)
EXAMPLE
The top left corner of the array:
1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, ...
3, 15, 21, 33, 39, 51, 57, 69, 75, 87, 93, 105, ...
9, 45, 63, 99, 117, 153, 171, 207, 225, 261, 279, 315, ...
27, 135, 189, 297, 351, 459, 513, 621, 675, 783, 837, 945, ...
81, 405, 567, 891, 1053, 1377, 1539, 1863, 2025, 2349, 2511, 2835, ...
243, 1215, 1701, 2673, 3159, 4131, 4617, 5589, 6075, 7047, 7533, 8505, ...
etc.
For n = 6, we have [A002260(6), A004736(6)] = [3, 1] (that is 6 corresponds to location 3,1 (row,col) in above table) and A(3,1) = A000244(3-1) * A007310(1) = 3^2 * 1 = 9.
For n = 9, we have [A002260(9), A004736(9)] = [3, 2] (9 corresponds to location 3,2) and A(3,2) = A000244(3-1) * A007310(2) = 3^2 * 5 = 9*5 = 45.
For n = 13, we have [A002260(13), A004736(13)] = [3, 3] (13 corresponds to location 3,3) and A(3,3) = A000244(3-1) * A007310(3) = 3^2 * 7 = 9*7 = 63.
For n = 23, we have [A002260(23), A004736(23)] = [2, 6] (23 corresponds to location 2,6) and A(2,6) = A000244(2-1) * A007310(6) = 3^1 * 17 = 51.
MAPLE
N:= 20:
B:= [seq(op([6*n+1, 6*n+5]), n=0..floor((N-1)/2))]:
[seq(seq(3^j*B[i-j], j=0..i-1), i=1..N)]; # Robert Israel, Jan 26 2015
PROG
(Scheme, two versions)
(define (A135765 n) (A135765bi (A002260 n) (A004736 n)))
(define (A135765bi row col) (* (A000244 (- row 1)) (A007310 col)))
(define (A135765 n) (+ -1 (* 2 (A254051 n))))
CROSSREFS
Row 1: A007310.
Column 1: A000244.
Cf. A007949 (row index), A126760 (column index).
Related arrays: A135764, A254051, A254055, A254101, A254102.
Sequence in context: A259068 A219336 A280235 * A222598 A221470 A030669
KEYWORD
easy,nonn,tabl
AUTHOR
Alford Arnold, Nov 28 2007
EXTENSIONS
Name amended and examples edited by Antti Karttunen, Jan 26 2015
STATUS
approved

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 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)