A331089 - OEIS

%I #13 Jan 09 2020 03:06:42

%S 1,2,3,15,20,21,44,50,54,55,56,57,75,104,110,111,115,128,141,152,175,

%T 207,264,291,304,308,335,351,363,376,377,380,392,398,399,435,452,455,

%U 534,584,594,605,623,654,735,740,744,753,795,804,875,884,897,924,964,968

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

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

%H Amiram Eldar, <a href="/A331089/b331089.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]];

%t nConsec = 2; neg = negFibQ /@ Range[nConsec]; seq = {}; c = 0;

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

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

%K nonn,base

%O 1,2

%A _Amiram Eldar_, Jan 08 2020