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 subsequence of A216893 where the sum of the prime divisors also equals twice a Fibonacci number.
Each term 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.
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 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:
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Michel Lagneau, Jan 30 2014
STATUS
approved