|
%I #29 Aug 29 2021 12:00:41
%S 1891,4181,8149,13201,15251,17711,40501,51841,64079,64681,67861,68251,
%T 78409,88601,88831,90061,96049,97921,115231,118441,145351,146611,
%U 153781,191351,197209,218791,219781,254321,272611,302101,303101
%N Semiprimes k that divide Fibonacci(k-1).
%C This is the semiprime (A001358) analog of A045468. Now A045468 has a very simple characterization: it consists of the primes ending in 1 or 9. Can one say anything about the present sequence?
%H Chai Wah Wu, <a href="/A177086/b177086.txt">Table of n, a(n) for n = 1..837</a>
%F {k: k is in A001358 and k|A000045(k-1)} = A069106 INTERSECTION A001358.
%e 46368/23 = 2016 = 2^5 * 3^2 * 7 so (24-1) | Fibonacci(24) but 24 is not semiprime, so is not in the sequence.
%e a(1) = 1891 = 31 * 61 is not in the sequence because 1891 divides Fibonacci(1891-1) = Fibonacci(1890).
%e a(21) = 146611 = 271 * 541 because 146611 | Fibonacci(146610).
%t Select[Range[310000],PrimeOmega[#]==2 && Divisible[Fibonacci[#-1],#]&] (* _Harvey P. Dale_, May 02 2016 *)
%Y Cf. A000040, A000045, A001358, A069106, A045468, A003631, A064739, A081264 (Fibonacci pseudoprimes).
%Y Cf. A177745 (semiprimes k that divide Fibonacci(k+1)).
%K nonn,easy
%O 1,1
%A _Jonathan Vos Post_, Dec 09 2010
|
