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 1-10 of 23 results. Next

A331820 Positive numbers k such that k and k + 1 are both negabinary-Niven numbers (A331728).

Original entry on oeis.org

1, 2, 3, 8, 14, 15, 20, 32, 35, 56, 62, 63, 68, 80, 90, 95, 124, 125, 128, 174, 184, 185, 215, 224, 244, 245, 248, 254, 255, 260, 272, 275, 300, 304, 305, 320, 335, 342, 468, 469, 484, 485, 512, 515, 544, 545, 552, 575, 594, 636, 720, 762, 784, 785, 804, 846, 896
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) = 11000 and 1 + 1 + 0 + 0 + 0 = 2 is a divisor of 8, and A039724(9) = 11001 and 1 + 1 + 0 + 0 + 1 = 3 is a divisor of 9.

Links

Crossrefs

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

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

A331822 Starts of runs of 3 consecutive positive negabinary-Niven numbers (A331728).

Original entry on oeis.org

1, 2, 14, 62, 124, 184, 244, 254, 304, 468, 484, 544, 784, 904, 964, 1022, 1084, 1098, 1144, 1264, 1265, 1308, 1448, 1504, 1518, 1924, 1938, 1984, 2044, 2104, 2105, 2358, 2888, 2944, 2945, 3064, 3198, 3248, 3424, 3544, 3604, 3618, 3664, 3828, 3844, 3904, 3964
Offset: 1

Views

Author

Amiram Eldar, Jan 27 2020

Keywords

Links

Crossrefs

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

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

A331824 Starts of runs of 4 consecutive positive negabinary-Niven numbers (A331728).

Original entry on oeis.org

1, 1264, 2104, 2944, 4624, 11888, 23768, 27312, 27728, 31688, 35648, 49144, 51488, 55448, 56704, 58384, 60072, 63424, 65104, 66784, 70144, 71288, 75248, 76452, 79208, 81904, 87128, 91088, 92832, 99008, 102968, 114848, 118808, 123904, 125592, 126728, 130624, 131044
Offset: 1

Views

Author

Amiram Eldar, Jan 27 2020

Keywords

Links

Crossrefs

Cf. A027615, A039724, A141769, A328211, A328215, A330933, A331728.

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 = 4; neg = negaBinNivenQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec+1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negaBinNivenQ[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

A331825 Positive numbers k such that -k, -(k + 1), -(k + 2), and -(k + 3) are 4 consecutive negative negabinary-Niven numbers (A331728).

Original entry on oeis.org

413, 2093, 3773, 4613, 7133, 7973, 8813, 10493, 11869, 15829, 16373, 23749, 30653, 31493, 34853, 35629, 37373, 39589, 40733, 49133, 51469, 54585, 55429, 63349, 64253, 65513, 67613, 70965, 75229, 91069, 98989, 102949, 103725, 106909, 110869, 114653, 129773, 131033
Offset: 1

Views

Author

Amiram Eldar, Jan 27 2020

Keywords

Links

Crossrefs

Cf. A027615, A039724, A141769, A328211, A328215, A330933, A331728, A331824.

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 = 4; neg = negaBinNivenQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec+1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negaBinNivenQ[k]}]; k++]; seq

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]

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

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

A342426 Niven numbers in base 3/2: numbers divisible by their sum of digits in fractional base 3/2 (A244040).

Original entry on oeis.org

1, 2, 6, 9, 14, 21, 40, 42, 56, 72, 84, 108, 110, 120, 126, 130, 143, 154, 156, 162, 165, 168, 169, 176, 180, 182, 189, 198, 220, 225, 231, 243, 252, 280, 288, 297, 306, 308, 320, 322, 330, 336, 348, 350, 364, 390, 423, 430, 432, 459, 460, 462, 480, 490, 504
Offset: 1

Views

Author

Amiram Eldar, Mar 11 2021

Keywords

Examples

			6 is a term since its representation in base 3/2 is 210 and 2 + 1 + 0 = 3 is a divisor of 6.
9 is a term since its representation in base 3/2 is 2100 and 2 + 1 + 0 + 0 = 3 is a divisor of 9.

Links

Crossrefs

Cf. A024629, A244040.
Subsequences: A342427, A342428, A342429.
Similar sequences: A005349 (decimal), A049445 (binary), A064150 (ternary), A064438 (quaternary), A064481 (base 5), A118363 (factorial), A328208 (Zeckendorf), A328212 (lazy Fibonacci), A331085 (negaFibonacci), A333426 (primorial), A334308 (base phi), A331728 (negabinary).

Programs

  • Mathematica
    s[0] = 0; s[n_] := s[n] = s[2*Floor[n/3]] + Mod[n, 3]; q[n_] := Divisible[n, s[n]]; Select[Range[500], q]

A342726 Niven numbers in base i-1: numbers that are divisible by the sum of their digits in base i-1.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 10, 12, 15, 16, 18, 20, 24, 25, 30, 32, 33, 35, 36, 40, 42, 44, 45, 48, 50, 54, 60, 64, 65, 66, 70, 77, 80, 88, 90, 96, 99, 100, 110, 112, 120, 124, 125, 126, 130, 140, 144, 145, 147, 150, 156, 160, 168, 170, 180, 182, 184, 185, 186, 190, 192
Offset: 1

Views

Author

Amiram Eldar, Mar 19 2021

Keywords

Comments

Numbers k that are divisible by A066323(k).
Equivalently, Niven numbers in base -4, since A066323(k) is also the sum of the digits of k in base -4.

Examples

			2 is a term since its representation in base i-1 is 1100 and 1+1+0+0 = 2 is a divisor of 2.
10 is a term since its representation in base i-1 is 111001100 and 1+1+1+0+0+1+1+0+0 = 5 is a divisor of 10.

Links

Crossrefs

Cf. A007608, A066321, A066323, A271472, A342725, A342727, A342728, A342729.
Similar sequences: A005349 (decimal), A049445 (binary), A064150 (ternary), A064438 (quaternary), A064481 (base 5), A118363 (factorial), A328208 (Zeckendorf), A328212 (lazy Fibonacci), A331085 (negaFibonacci), A333426 (primorial), A334308 (base phi), A331728 (negabinary), A342426 (base 3/2).

Programs

  • Mathematica
    v = {{0, 0, 0, 0}, {0, 0, 0, 1}, {1, 1, 0, 0}, {1, 1, 0, 1}}; q[n_] := Divisible[n, Total[Flatten @ v[[1 + Reverse @ Most[Mod[NestWhileList[(# - Mod[#, 4])/-4 &, n, # != 0 &], 4]]]]]]; Select[Range[200], q]
Showing 1-10 of 23 results. Next

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