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

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

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.

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 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

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