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A236694 Fibonacci numbers such that the difference between the greatest prime divisor and the smallest prime divisor equals twice a Fibonacci number. 0

%I

%S 21,55,377,17711,121393,5702887,19740274219868223167

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

%C The corresponding indices of the Fibonacci numbers are 8, 10, 14, 22, 26, 34, 94.

%C Property of this sequence: a(n) is a subset of A216893 where the sum of the prime divisors equals also twice a Fibonacci number.

%C Each number of this sequence is semiprime p*q, q>p primes with p+q = f1 + f2 and q-p = f1-f2, where f1 and f2 are Fibonacci numbers => f1 = (p+q)/2 and f2=(q-p)/2.

%e 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).

%p 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 nn-3 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:

%Y Cf. A008472, A000045, A216893.

%K nonn,hard

%O 1,1

%A _Michel Lagneau_, Jan 30 2014

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Last modified December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)