A331089 -id:A331089 - cp's OEIS frontend

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

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

Amiram Eldar, Jan 27 2020

			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.

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

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

A331092 Positive numbers k such that k and k + 1 are both positive negaFibonacci-Niven numbers (A331085) and -k and -(k + 1) are both negative negaFibonacci-Niven numbers (A331088).

Original entry on oeis.org

1, 744, 875, 924, 1115, 1575, 1704, 1955, 2904, 3815, 5495, 5844, 6125, 6335, 6824, 7136, 7314, 8154, 8225, 8360, 8784, 9414, 10535, 10744, 10935, 11976, 12047, 13194, 13404, 13475, 18024, 19368, 19943, 20615, 21791, 22224, 22560, 23807, 24143, 24576, 25752, 26424, 26999

Offset: 1

Amiram Eldar, Jan 08 2020

Positive numbers k such that both k and k + 1 are in A331091.

Amiram Eldar, Table of n, a(n) for n = 1..10000

Intersection of A331086 and A331089.

Cf. A331085, A331088, A331091.

ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
f[1] = 1; f[n_] := If[n > 0, i = ind[n - 1]; If[EvenQ[i], i++]; i, i = ind[-n]; If[OddQ[i], i++]; i];
negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
negFibQ[n_] := Divisible[n, negaFibTermsNum[n]] && Divisible[n, negaFibTermsNum[-n]];
nConsec = 2; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0; k = nConsec + 1; While[c < 45, If[And @@ neg, c++; AppendTo[seq, k - nConsec]]; neg = Join[Rest[neg], {negFibQ[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

Amiram Eldar, Jan 27 2020

			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.

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

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

cp's OEIS Frontend

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

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A331092 Positive numbers k such that k and k + 1 are both positive negaFibonacci-Niven numbers (A331085) and -k and -(k + 1) are both negative negaFibonacci-Niven numbers (A331088).

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

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