A328213 - OEIS

%I #11 Jan 05 2025 19:51:41

%S 1,15,35,369,549,710,890,1089,1989,2196,2629,2951,3311,3679,3684,4927,

%T 5268,5291,5488,5603,5775,5819,5928,5940,6524,7072,7364,7403,7475,

%U 7500,7657,7812,8567,9254,9360,9372,9383,9477,9841,10205,10304,10360,11816,13299,13454

%N Numbers m such that m and m+1 are consecutive lazy-Fibonacci-Niven numbers (A328212).

%H Amiram Eldar, <a href="/A328213/b328213.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 15 is in the sequence since both 15 and 16 are in A328212: A112310(15) = 3 is a divisor of 15, and A112310(16) = 4 is a divisor of 16.

%t ooQ[n_] := Module[{k = n}, While[k > 3, If[Divisible[k, 4], Return[True], k = Quotient[k, 2]]]; False]; c = 0; cn = 0; k = 1; s = {}; v = Table[-1, {2}]; While[cn < 45, If[! ooQ[k], c++; d = Total@IntegerDigits[k, 2]; If[Divisible[c, d], v = Join[Rest[v], {c}]; If[AllTrue[Differences[v], # == 1 &], cn++; AppendTo[s, c - 1]]]]; k++]; s

%Y Cf. A112310, A328212.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 07 2019