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Lazy-Fibonacci-Niven numbers: numbers divisible by the number of terms in their lazy Fibonacci representation (A112310).
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%I #9 Jan 05 2025 19:51:41

%S 1,2,4,6,9,12,15,16,28,30,35,36,48,55,60,70,72,75,78,84,90,102,105,

%T 114,119,126,133,144,147,154,156,161,168,180,182,184,192,198,203,208,

%U 216,224,238,240,245,252,259,264,266,272,280,296,301,304,308,315,320,322

%N Lazy-Fibonacci-Niven numbers: numbers divisible by the number of terms in their lazy Fibonacci representation (A112310).

%H Amiram Eldar, <a href="/A328212/b328212.txt">Table of n, a(n) for n = 1..10000</a>

%H Helen G. Grundman, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/45-3/grundman.pdf">Consecutive Zeckendorf-Niven and lazy-Fibonacci-Niven numbers</a>, Fibonacci Quarterly, Vol. 45, No. 3 (2007), pp. 272-276.

%e 6 is in the sequence since A112310(6) = 3 and 3 is a divisor of 6.

%t ooQ[n_] := Module[{k = n}, While[k > 3, If[Divisible[k, 4], Return[True], k = Quotient[k, 2]]]; False]; c = 0; s = {}; Do[If[! ooQ[k], c++; d = Total @ IntegerDigits[k, 2]; If[Divisible[c, d], AppendTo[s, c]]], {k, 1, 2000}]; s

%Y Cf. A004753, A005349, A112310.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 07 2019