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.

A331827 Positive negabinary-Niven numbers k (A331728) such that -k is a negative negabinary-Niven number (A331819).

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 12, 15, 16, 18, 20, 24, 28, 30, 32, 33, 36, 40, 42, 48, 54, 56, 60, 63, 64, 66, 68, 72, 78, 80, 84, 90, 96, 100, 102, 108, 112, 114, 120, 124, 126, 128, 129, 132, 136, 138, 140, 144, 150, 156, 160, 162, 168, 174, 175, 180, 186, 192, 198, 200
Offset: 1

Views

Author

Amiram Eldar, Jan 28 2020

Keywords

Comments

Positive numbers k that are divisible by the sums of digits in the negabinary representations of both k and -k.
All the powers of 2 above 1 are terms.

Links

Crossrefs

Intersection of A331728 and A331819.
Cf. A330711, A331091.

Programs

  • Mathematica
    negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; seqQ[n_] := And @@ (Divisible[n, negaBinWt[#]] & /@ {-n, n}); Select[Range[200], seqQ]

A331829 Positive numbers k such that k and k + 1 are both positive negabinary-Niven numbers (A331728) and -k and -(k + 1) are both negative negabinary-Niven numbers (A331819).

Original entry on oeis.org

2, 3, 8, 15, 32, 63, 128, 174, 245, 255, 512, 1023, 1085, 1295, 1505, 1854, 1925, 2048, 2744, 3248, 3303, 3752, 4025, 4095, 4760, 4815, 4865, 5004, 5319, 5768, 6327, 6776, 7104, 7784, 7944, 8154, 8192, 8574, 8792, 8855, 9800, 10254, 10808, 11312, 11816, 11871
Offset: 1

Views

Author

Amiram Eldar, Jan 28 2020

Keywords

Comments

Positive numbers k such that both k and k + 1 are in A331827.
Numbers of the form 2^(2*k+1) and 2^(2*k) - 1 are terms.

Links

Crossrefs

Intersection of A331820 and A331821.
Cf. A331092, A331728, A331819, A331827.

Programs

  • Mathematica
    negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; negBinQ[n_] := And @@ (Divisible[n, negaBinWt[#]] & /@ {-n, n}); nConsec = 2; neg = negBinQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec + 1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negBinQ[k]}]; k++]; seq

A331821 Positive numbers k such that -k and -(k + 1) are both negabinary-Niven numbers (A331728).

Original entry on oeis.org

2, 3, 8, 9, 15, 24, 27, 32, 33, 39, 54, 55, 63, 77, 111, 114, 115, 123, 128, 129, 135, 144, 159, 174, 175, 203, 234, 235, 245, 255, 264, 294, 295, 329, 370, 371, 384, 413, 414, 415, 444, 447, 474, 475, 495, 504, 507, 512, 513, 519, 534, 535, 543, 580, 581, 624
Offset: 1

Views

Author

Amiram Eldar, Jan 27 2020

Keywords

Examples

			8 is a term since both -8 and -(8 + 1) = -9 are negabinary-Niven numbers: A039724(-8) = 1000 and 1 + 0 + 0 + 0 = 1 is a divisor of 8, and A039724(-9) = 1011 and 1 + 0 + 1 + 1 = 3 is a divisor of 9.

Links

Crossrefs

Cf. A005352, A027615, A039724, A328209, A328213, A330927, A330931, A331086, A331089, A331728, A331819, A331820.

Programs

  • Mathematica
    negaBinWt[n_] := negaBinWt[n] = If[n == 0, 0, negaBinWt[Quotient[n - 1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[-n]]; c = 0; k = 1; s = {}; v = Table[-1, {2}]; While[c < 60, If[negaBinNivenQ[k], v = Join[Rest[v], {k}]; If[AllTrue[Differences[v], # == 1 &], c++; AppendTo[s, k - 1]]]; k++]; s

A331823 Positive numbers k such that -k, -(k + 1), and -(k + 2) are 3 consecutive negative negabinary-Niven numbers (A331728).

Original entry on oeis.org

2, 8, 32, 54, 114, 128, 174, 234, 294, 370, 413, 414, 474, 512, 534, 580, 654, 774, 894, 954, 1000, 1014, 1134, 1430, 1734, 1794, 1840, 1854, 1914, 1974, 2034, 2048, 2093, 2094, 2154, 2214, 2334, 2574, 2680, 2694, 2814, 2870, 3054, 3100, 3520, 3773, 3774, 3834
Offset: 1

Views

Author

Amiram Eldar, Jan 27 2020

Keywords

Links

Crossrefs

Cf. A005352, A027615, A039724, A154701, A328210, A328214, A330932, A331087, A331090, A331728, A331819, A331822.

Programs

  • Mathematica
    negaBinWt[n_] := negaBinWt[n] = If[n == 0, 0, negaBinWt[Quotient[n - 1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[-n]]; nConsec = 3; neg = negaBinNivenQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec+1; While[c < 50, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negaBinNivenQ[k]}]; k++]; seq
Showing 1-4 of 4 results.

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

Content is available under The OEIS End-User License Agreement.