A092249 Positions of the integers in the standard diagonal enumeration of the rationals (with the integers in the first column and diagonals moving up to the right).
1, 2, 4, 6, 10, 12, 18, 22, 28, 32, 42, 46, 58, 64, 72, 80, 96, 102, 120, 128, 140, 150, 172, 180, 200, 212, 230, 242, 270, 278, 308, 324, 344, 360, 384, 396, 432, 450, 474, 490, 530, 542, 584, 604, 628, 650, 696, 712, 754, 774, 806, 830, 882, 900, 940, 964
Offset: 1
Keywords
Examples
The first few terms of the full enumeration are 1, 2, 1/2, 3, 1/3, 4, 3/2, 2/3, 1/4, 5, giving a(n) = 1, 2, 4, 6, 10,... Contribution from _R. J. Mathar_, Jul 20 2009: (Start) The positions in the first column of the table ....1..1/2..1/3..1/4..1/5..1/6..1/7..1/8..1/9.1/10.1/11.1/12 ....2.......2/3.......2/5.......2/7.......2/9......2/11..... ....3..3/2.......3/4..3/5.......3/7..3/8......3/10.3/11..... ....4.......4/3.......4/5.......4/7.......4/9......4/11..... ....5..5/2..5/3..5/4.......5/6..5/7..5/8..5/9......5/11.5/12 ....6.................6/5.......6/7................6/11..... ....7..7/2..7/3..7/4..7/5..7/6.......7/8..7/9.7/10.7/11.7/12 ....8.......8/3.......8/5.......8/7.......8/9......8/11..... ....9..9/2.......9/4..9/5.......9/7..9/8......9/10.9/11..... ...10......10/3................10/7......10/9.....10/11..... ...11.11/2.11/3.11/4.11/5.11/6.11/7.11/8.11/911/10.....11/12 ...12................12/5......12/7...............12/11..... if scanned along rising antidiagonals, as defined by the ratios A038566(i)/A020653(i). (End)
Links
- Paolo Xausa, Table of n, a(n) for n = 1..10000
- N. J. A. Sloane, Families of Essentially Identical Sequences, Mar 24 2021 (Includes this sequence)
Programs
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Mathematica
Accumulate[EulerPhi[Range[100]]] (* Paolo Xausa, Oct 19 2023 *)
Extensions
a(11) and a(12) corrected by R. J. Mathar, Jul 20 2009
Incorrect recurrence formula removed by R. J. Mathar, Jul 29 2009
More terms (using A002088) from Michel Marcus, Sep 10 2018
Comments