A331088 -id:A331088 - cp's OEIS frontend

A331089 Positive numbers k such that -k and -(k + 1) are both negative negaFibonacci-Niven numbers (A331088).

1, 2, 3, 15, 20, 21, 44, 50, 54, 55, 56, 57, 75, 104, 110, 111, 115, 128, 141, 152, 175, 207, 264, 291, 304, 308, 335, 351, 363, 376, 377, 380, 392, 398, 399, 435, 452, 455, 534, 584, 594, 605, 623, 654, 735, 740, 744, 753, 795, 804, 875, 884, 897, 924, 964, 968

Offset: 1

Amiram Eldar, Jan 08 2020

The Fibonacci numbers F(6*k + 2) and F(6*k + 4) are terms.

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

Cf. A328209, A328213, A330927, A330931, A331086, A331088.

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]];
nConsec = 2; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0;
k = nConsec+1; While[c < 55, If[And @@ neg, c++; AppendTo[seq, k - nConsec]];neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq

A331090 Positive numbers k such that -k, -(k + 1), and -(k + 2) are 3 consecutive negative negaFibonacci-Niven numbers (A331088).

Original entry on oeis.org

1, 2, 20, 54, 55, 56, 110, 376, 398, 974, 986, 1084, 1744, 2464, 2524, 3304, 3870, 5223, 5718, 6095, 6124, 6184, 6663, 6764, 6844, 7142, 7684, 9035, 9124, 10590, 11598, 11975, 12606, 13444, 13504, 14284, 14915, 17164, 17643, 17710, 17714, 17824, 17884, 18698, 18905, 19494, 23191, 24243, 24785, 25542, 26382, 27390, 29644, 34278, 35464

Offset: 1

Amiram Eldar, Jan 08 2020

Numbers of the form F(6*k + 2) - 1 and F(6*k + 4) - 1, where F(m) is the m-th Fibonacci number, are terms.

If m is of the form F(k) - 1, where k > 2 is congruent to {2, 10} mod 24, then {-m, -(m + 1), -(m + 2), -(m + 3), -(m + 4)} are 5 consecutive negative negaFibonacci-Niven numbers.

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

Cf. A000045, A154701, A269819, A328210, A328214, A330932, A331087, A331088.

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]];
nConsec = 3; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0;
k = nConsec+1; While[c < 55, If[And @@ neg, c++; AppendTo[seq, k - nConsec]];neg = Join[Rest[neg], {negFibQ[k]}]; k++]; seq

A331091 Positive negaFibonacci-Niven numbers k (A331085) such that -k is a negative negaFibonacci-Niven number (A331088).

Original entry on oeis.org

1, 2, 4, 6, 12, 18, 24, 27, 30, 36, 48, 55, 60, 72, 84, 90, 96, 100, 108, 110, 112, 116, 120, 144, 150, 156, 172, 176, 180, 184, 192, 196, 208, 228, 234, 240, 246, 252, 260, 264, 288, 300, 305, 320, 328, 330, 336, 340, 360, 372, 378, 384, 396, 400, 415, 420, 460, 468, 475, 480, 492

Offset: 1

Amiram Eldar, Jan 08 2020

Positive numbers k that are divisible by the number of terms in the negaFibonacci representations of both k and -k (A215022 and A215023, respectively).

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

Intersection of A331085 and A331088.

Cf. A215022, A215023, A330711.

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];
Select[Range[500], Divisible[#, negaFibTermsNum[#]] && Divisible[#, negaFibTermsNum[-#]] &]

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

A331728 Negabinary-Niven numbers: numbers divisible by the sum of digits in their negabinary representation (A027615).

Original entry on oeis.org

1, 2, 3, 4, 6, 8, 9, 12, 14, 15, 16, 18, 20, 21, 24, 28, 30, 32, 33, 35, 36, 40, 42, 48, 50, 52, 54, 56, 57, 60, 62, 63, 64, 66, 68, 69, 72, 76, 78, 80, 81, 84, 88, 90, 91, 95, 96, 100, 102, 108, 110, 112, 114, 120, 124, 125, 126, 128, 129, 132, 136, 138, 140

Offset: 1

Amiram Eldar, Jan 27 2020

			6 is a term since A039724(6) = 11010 and 1 + 1 + 0 + 1 + 0 = 3 is a divisor of 6.

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

Cf. A027615, A039724, A005349, A049445, A328208, A328212, A331085, A331088.

negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[n]]; Select[Range[100], negaBinNivenQ]

A331819 Positive numbers k such that -k is a negative negabinary-Niven number, i.e., divisible by the sum of digits of its negabinary representation (A027615).

Original entry on oeis.org

2, 3, 4, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 28, 30, 32, 33, 34, 36, 39, 40, 42, 44, 48, 54, 55, 56, 60, 63, 64, 66, 68, 70, 72, 77, 78, 80, 84, 90, 92, 96, 100, 102, 104, 108, 111, 112, 114, 115, 116, 120, 123, 124, 126, 128, 129, 130, 132, 135, 136, 138, 140

Offset: 1

Amiram Eldar, Jan 27 2020

			6 is a term since A039724(-6) = 1110 and 1 + 1 + 1 + 0 = 3 is a divisor of 6.

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

Cf. A005352, A027615, A039724, A005349, A049445, A328208, A328212, A331085, A331088, A331728.

negaBinWt[n_] := negaBinWt[n] = If[n==0, 0, negaBinWt[Quotient[n-1, -2]] + Mod[n, 2]]; negaBinNivenQ[n_] := Divisible[n, negaBinWt[-n]]; Select[Range[100], negaBinNivenQ]

cp's OEIS Frontend

A331089 Positive numbers k such that -k and -(k + 1) are both negative negaFibonacci-Niven numbers (A331088).

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A331090 Positive numbers k such that -k, -(k + 1), and -(k + 2) are 3 consecutive negative negaFibonacci-Niven numbers (A331088).

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A331091 Positive negaFibonacci-Niven numbers k (A331085) such that -k is a negative negaFibonacci-Niven number (A331088).

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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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A331728 Negabinary-Niven numbers: numbers divisible by the sum of digits in their negabinary representation (A027615).

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A331819 Positive numbers k such that -k is a negative negabinary-Niven number, i.e., divisible by the sum of digits of its negabinary representation (A027615).

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