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A331088 Positive numbers k such that -k is a negative negaFibonacci-Niven number, i.e., divisible by the number of terms in its negaFibonacci representation (A331084).

%I A331088 #11 Jan 09 2020 03:06:38
%S A331088 1,2,3,4,6,8,12,15,16,18,20,21,22,24,27,30,36,42,44,45,48,50,51,54,55,
%T A331088 56,57,58,60,66,72,75,76,80,84,90,92,96,100,104,105,108,110,111,112,
%U A331088 115,116,120,124,126,128,129,132,136,138,141,142,144,150,152,153,156,168,170,172,175,176,180,184,186,190,192,196,198
%N A331088 Positive numbers k such that -k is a negative negaFibonacci-Niven number, i.e., divisible by the number of terms in its negaFibonacci representation (A331084).
%C A331088 The k-th Fibonacci number is a term for all even k, since its negaFibonacci representation is 1 followed by (k-1) zeros.
%H A331088 Amiram Eldar, <a href="/A331088/b331088.txt">Table of n, a(n) for n = 1..10000</a>
%e A331088 4 is a term since the negaFibonacci representation of -4 is 1010 whose sum of digits is 1 + 0 + 1 + 0 = 2 which is a divisor of 4.
%t A331088 ind[n_] := Floor[Log[Abs[n]*Sqrt[5] + 1/2]/Log[GoldenRatio]];
%t A331088 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 A331088 negaFibTermsNum[n_] := Module[{k = n, s = 0}, While[k != 0, i = f[k]; s += 1; k -= Fibonacci[-i]]; s];
%t A331088 Select[Range[200], Divisible[#, negaFibTermsNum[-#]] &]
%Y A331088 Cf. A005349, A215023, A328208, A328212, A331083, A331084, A331085.
%K A331088 nonn,base
%O A331088 1,2
%A A331088 _Amiram Eldar_, Jan 08 2020