This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A135765 #25 Feb 03 2015 16:09:49 %S A135765 1,5,3,7,15,9,11,21,45,27,13,33,63,135,81,17,39,99,189,405,243,19,51, %T A135765 117,297,567,1215,729,23,57,153,351,891,1701,3645,2187,25,69,171,459, %U A135765 1053,2673,5103,10935,6561,29,75,207,513,1377,3159,8019,15309,32805 %N 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), ... %C A135765 The Table can be constructed by multiplying sequence A000244 by A007310. %C A135765 From _Antti Karttunen_, Jan 26 2015: (Start) %C A135765 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. %C A135765 Each odd number n occurs here in position A(A007949(n), A126760(n)). %C A135765 Compare also to A135764. %C A135765 (End) %H A135765 Antti Karttunen, <a href="/A135765/b135765.txt">Table of n, a(n) for n = 1..10440; the first 144 antidiagonals of array</a> %H A135765 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a> %F A135765 From _Antti Karttunen_, Jan 26 2015: (Start) %F A135765 With both row and col starting from 1: %F A135765 A(row, col) = A000244(row-1) * A007310(col) = 3^(row-1) * A007310(col). %F A135765 a(n) = (2*A254051(n))-1. %F A135765 a(n) = A003961(A254053(n)). %F A135765 Above in array form: %F A135765 A(row,col) = A003961(A254053(row,col)) = A003961(A135764(row,A249745(col))). %F A135765 (End) %e A135765 The top left corner of the array: %e A135765 1, 5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, ... %e A135765 3, 15, 21, 33, 39, 51, 57, 69, 75, 87, 93, 105, ... %e A135765 9, 45, 63, 99, 117, 153, 171, 207, 225, 261, 279, 315, ... %e A135765 27, 135, 189, 297, 351, 459, 513, 621, 675, 783, 837, 945, ... %e A135765 81, 405, 567, 891, 1053, 1377, 1539, 1863, 2025, 2349, 2511, 2835, ... %e A135765 243, 1215, 1701, 2673, 3159, 4131, 4617, 5589, 6075, 7047, 7533, 8505, ... %e A135765 etc. %e A135765 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. %e A135765 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. %e A135765 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. %e A135765 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. %p A135765 N:= 20: %p A135765 B:= [seq(op([6*n+1,6*n+5]),n=0..floor((N-1)/2))]: %p A135765 [seq(seq(3^j*B[i-j],j=0..i-1),i=1..N)]; # _Robert Israel_, Jan 26 2015 %o A135765 (Scheme, two versions) %o A135765 (define (A135765 n) (A135765bi (A002260 n) (A004736 n))) %o A135765 (define (A135765bi row col) (* (A000244 (- row 1)) (A007310 col))) %o A135765 (define (A135765 n) (+ -1 (* 2 (A254051 n)))) %Y A135765 Row 1: A007310. %Y A135765 Column 1: A000244. %Y A135765 Cf. A007949 (row index), A126760 (column index). %Y A135765 Cf. also A000265, A002260, A003961, A004736, A005408, A165355, A249745. %Y A135765 Related arrays: A135764, A254051, A254055, A254101, A254102. %K A135765 easy,nonn,tabl %O A135765 1,2 %A A135765 _Alford Arnold_, Nov 28 2007 %E A135765 Name amended and examples edited by _Antti Karttunen_, Jan 26 2015