A331091 -id:A331091 - cp's OEIS frontend

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).

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

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

Amiram Eldar, Jan 28 2020

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.

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

Intersection of A331728 and A331819.

Cf. A330711, A331091.

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]

cp's OEIS Frontend

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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