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A114419 a(n) is the smallest number k such that Fibonacci(k) is a multiple of primorial(n). 2

%I #25 Feb 24 2024 01:13:22

%S 3,12,60,120,120,840,2520,2520,2520,2520,2520,47880,47880,526680,

%T 1053360,3160080,91642320,91642320,1557919440,1557919440,57643019280,

%U 749359250640,749359250640,749359250640,5245514754480,26227573772400

%N a(n) is the smallest number k such that Fibonacci(k) is a multiple of primorial(n).

%C Because the Fibonacci numbers form a divisibility sequence, each term of this sequence is a multiple of the previous term. The multiple can be computed using A001602. - _T. D. Noe_, May 04 2009

%H Zak Seidov, <a href="/A114419/b114419.txt">Table of n, a(n) for n = 1..100</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

%F a(n) = {min j: A002110(n) | A000045(j)}. - _R. J. Mathar_, Jan 31 2008

%F a(n) = lcm(A001602(1),...,A001602(n)). - _T. D. Noe_, May 04 2009

%e a(2)=12 because 12th Fibonacci number (144) is the smallest Fibonacci number which is a multiple of primorial(2), i.e., 6.

%o (PARI) a(n) = {prn = prod(k=1, n, prime(k)); k = 1; while(fibonacci(k) % prn, k++); k;} \\ _Michel Marcus_, Jan 13 2016

%Y Cf. A002110, A000045.

%Y Cf. A267095.

%K nonn

%O 1,1

%A _Shyam Sunder Gupta_, Feb 12 2006

%E a(1) corrected and a(14) added by _R. J. Mathar_, Jan 31 2008

%E a(14)-a(18) from _Donovan Johnson_, Sep 03 2008

%E Extended by _T. D. Noe_, May 04 2009

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Last modified September 3 02:10 EDT 2024. Contains 375649 sequences. (Running on oeis4.)