

A236694


Fibonacci numbers such that the difference between the greatest prime divisor and the smallest prime divisor equals twice a Fibonacci number.


0




OFFSET

1,1


COMMENTS

The corresponding indices of the Fibonacci numbers are 8, 10, 14, 22, 26, 34, 94.
Property of this sequence: a(n) is a subset of A216893 where the sum of the prime divisors equals also twice a Fibonacci number.
Each number of this sequence is semiprime p*q, q>p primes with p+q = f1 + f2 and qp = f1f2, where f1 and f2 are Fibonacci numbers => f1 = (p+q)/2 and f2=(qp)/2.


LINKS

Table of n, a(n) for n=1..7.


EXAMPLE

121393 = F(26) = 233*521 is in the sequence because 521  233 = 288 = 2*F(12), but also 233 + 521 = 2*377 = 2*F(14).


MAPLE

with(numtheory):nn:=200:with(combinat, fibonacci):lst:={}:for i from 3 to nn do:lst:=lst union {fibonacci(i)}:od:for n from 1 to nn3 do:f:=lst[n]: x:=factorset(f):n1:=nops(x): s:=x[n1]x[1]:if {s/2} intersect lst = {s/2} then printf(`%d, `, f):else fi:od:


CROSSREFS

Cf. A008472, A000045, A216893.
Sequence in context: A067431 A083676 A264104 * A292368 A301607 A145719
Adjacent sequences: A236691 A236692 A236693 * A236695 A236696 A236697


KEYWORD

nonn,hard


AUTHOR

Michel Lagneau, Jan 30 2014


STATUS

approved



