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A177086 Semiprimes k that divide Fibonacci(k-1). 2
1891, 4181, 8149, 13201, 15251, 17711, 40501, 51841, 64079, 64681, 67861, 68251, 78409, 88601, 88831, 90061, 96049, 97921, 115231, 118441, 145351, 146611, 153781, 191351, 197209, 218791, 219781, 254321, 272611, 302101, 303101 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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?

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..837

FORMULA

{k: k is in A001358 and k|A000045(k-1)} = A069106 INTERSECTION A001358.

EXAMPLE

46368/23 = 2016 = 2^5 * 3^2 * 7 so (24-1) | Fibonacci(24) but 24 is not semiprime, so is not in the sequence.

a(1) = 1891 = 31 * 61 is not in the sequence because 1891 divides Fibonacci(1891-1) = Fibonacci(1890).

a(21) = 146611 = 271 * 541 because 146611 | Fibonacci(146610).

MATHEMATICA

Select[Range[310000], PrimeOmega[#]==2 && Divisible[Fibonacci[#-1], #]&] (* Harvey P. Dale, May 02 2016 *)

CROSSREFS

Cf. A000040, A000045, A001358, A069106, A045468, A003631, A064739, A081264 (Fibonacci pseudoprimes).

Cf. A177745 (semiprimes k that divide Fibonacci(k+1)).

Sequence in context: A251821 A151773 A020321 * A254285 A035869 A045198

Adjacent sequences:  A177083 A177084 A177085 * A177087 A177088 A177089

KEYWORD

nonn,easy

AUTHOR

Jonathan Vos Post, Dec 09 2010

STATUS

approved

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Last modified October 5 13:32 EDT 2022. Contains 357258 sequences. (Running on oeis4.)