A331092 - OEIS

%I #12 Jan 09 2020 03:06:56

%S 1,744,875,924,1115,1575,1704,1955,2904,3815,5495,5844,6125,6335,6824,

%T 7136,7314,8154,8225,8360,8784,9414,10535,10744,10935,11976,12047,

%U 13194,13404,13475,18024,19368,19943,20615,21791,22224,22560,23807,24143,24576,25752,26424,26999

%N 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).

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

%H Amiram Eldar, <a href="/A331092/b331092.txt">Table of n, a(n) for n = 1..10000</a>

%t ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];

%t 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];

%t negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];

%t negFibQ[n_] := Divisible[n, negaFibTermsNum[n]] && Divisible[n, negaFibTermsNum[-n]];

%t 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

%Y Intersection of A331086 and A331089.

%Y Cf. A331085, A331088, A331091.

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Jan 08 2020