cp's OEIS Frontend

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.

Showing 1-4 of 4 results.

A277725 Intersection of A158919 and A277723.

Original entry on oeis.org

0, 12, 18, 31, 49, 62, 68, 80, 93, 99, 112, 130, 136, 143, 161, 174, 180, 211, 217, 224, 242, 248, 255, 261, 286, 292, 323, 329, 336, 342, 354, 360, 367, 373, 404, 410, 423, 435, 441, 448, 454, 472, 485, 491, 516, 522, 535, 553, 560, 566, 572, 584, 597, 603, 616, 634, 640, 647, 665, 678, 684, 709, 715
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2016

Keywords

Comments

See A277728 for discussion.

Crossrefs

Cf. A003144, A003145, A003146, A058265, A158919, A275926, A276799, A276800, A277722, A277723, A277724, A277725, A277726, A277727, A277728.

A277726 Intersection of A277722 and A277723.

Original entry on oeis.org

0, 6, 37, 43, 74, 87, 118, 155, 186, 192, 199, 230, 236, 267, 280, 304, 311, 317, 348, 385, 392, 416, 429, 460, 466, 497, 504, 510, 541, 578, 622, 659, 690, 696, 703, 734, 740, 771, 784, 808, 815, 852, 889, 896, 920, 933, 964, 970, 1001, 1008, 1014, 1045, 1082, 1126, 1163, 1194, 1200, 1207, 1238, 1244, 1275, 1288, 1312, 1319, 1356, 1387, 1393, 1400, 1424
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2016

Keywords

Comments

See A277728 for discussion.

Crossrefs

Cf. A003144, A003145, A003146, A058265, A158919, A275926, A276799, A276800, A277722, A277723, A277724, A277725, A277726, A277727, A277728.

Programs

  • Maple
    Digits := 120;
isA277722 := proc(n)
    a276800 :=  3.3829757679062374941227085364550345869493820437485761820195626772353718960099402922235933340043661396041006 ;
    for x from floor((n-3)/a276800) to (n+3)/a276800 do
        if floor(x*a276800) = n then
            return true;
        end if;
    end do:
    return false;
end proc:
isA277723 := proc(n)
    a276801 :=  6.2222625231203986266745611011083211873735607898461684287983213166395751180919067179620287534326731537460804;
    for x from floor((n-3)/a276801) to (n+3)/a276801 do
        if floor(x*a276801) = n then
            return true;
        end if;
    end do:
    return false;
end proc:
isA277726 := proc(n)
    isA277722(n) and isA277723(n) ;
end proc:
for n from 0 to 8000 do
    if isA277726(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Nov 02 2016

Extensions

Corrected by R. J. Mathar, Nov 01 2016

A277727 Union of A158919, A277722, A277723.

Original entry on oeis.org

0, 1, 3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 16, 18, 20, 22, 23, 24, 25, 27, 29, 30, 31, 33, 34, 36, 37, 38, 40, 42, 43, 44, 45, 47, 49, 50, 51, 53, 54, 55, 56, 57, 58, 60, 62, 64, 66, 67, 68, 69, 71, 73, 74, 75, 77, 79, 80, 81, 82, 84, 86, 87, 88, 90, 91, 93, 94, 95, 97, 98, 99, 101, 103, 104, 105, 106
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2016

Keywords

Comments

See A277728 for discussion.

Crossrefs

Cf. A003144, A003145, A003146, A058265, A158919, A275926, A276799, A276800, A277722, A277723, A277724, A277725, A277726, A277727, A277728.

A277728 Numbers not in any of A158919, A277722, A277723.

Original entry on oeis.org

2, 4, 8, 15, 17, 19, 21, 26, 28, 32, 35, 39, 41, 46, 48, 52, 59, 61, 63, 65, 70, 72, 76, 78, 83, 85, 89, 92, 96, 100, 102, 107, 109, 113, 116, 120, 122, 127, 129, 133, 140, 144, 146, 151, 153, 157, 159, 164, 166, 170, 173, 177, 181, 184, 188, 190, 195, 197, 201, 203, 208, 210, 212, 214, 221
Offset: 1

Views

Author

N. J. A. Sloane, Oct 30 2016

Keywords

Comments

Let tau be the tribonacci constant (A058265). Although 1/tau + 1/tau^2 + 1/tau^3 = 1, by Uspensky's 1927 theorem, the three sequences floor(n*tau) (A158919), floor(n*tau^2) (A277722), and floor(n*tau^3) (A277723) cannot form a partition of the nonnegative integers. (Compare Beatty's theorem.)
Entries A277724-A277727 investigate how these three sequences meet, and the present sequence gives the numbers not in any of the three sequences. Any two of the three sequences have a nontrivial intersection, while the intersection of all three is {0}.
On the other hand, the three sequences A003144, A003145, A003146, which arise from the tribonacci word, DO form a partition of the positive integers and are closely connected with the three sequences mentioned in the definition.
It would be nice to have b-files for all the sequences mentioned here. (Many do, but some do not.)

Links

Crossrefs

Cf. A003144, A003145, A003146, A058265, A158919, A184820, A277722, A277723, A277724, A277725, A277726, A277727.

Programs

  • Mathematica
    maxTerm = 10000;
a19[n_] := Floor[n*Root[#^3 - #^2 - # - 1&, 1]];
a22[n_] := Floor[n*Root[#^3 - 3 #^2 - # - 1&, 1]];
a23[n_] := Floor[n*Root[#^3 - 7 #^2 + 5 # - 1&, 1]];
A19 = Reap[k = 1; While[a19[k] <= maxTerm, Sow[a19[k++]]]][[2, 1]];
A22 = Reap[k = 1; While[a22[k] <= maxTerm, Sow[a22[k++]]]][[2, 1]];
A23 = Reap[k = 1; While[a23[k] <= maxTerm, Sow[a23[k++]]]][[2, 1]];
Select[Range[maxTerm], FreeQ[A19, #] && FreeQ[A22, #] && FreeQ[A23, #]&] (* Jean-François Alcover, Dec 06 2018 *)
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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