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A242103 Numbers m such that m^2 - 1 is the product of three distinct Fibonacci numbers > 1. 0
7, 9, 11, 14, 29, 76, 121, 199, 329, 521, 659, 1364, 3571, 4523, 7307, 9349, 24476, 64079, 167761, 212533, 439204, 1149851, 3010349, 7881196, 20633239, 54018521, 141422324, 370248451, 969323029, 2537720636, 6643838879, 17393796001, 45537549124, 119218851371 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Conjecture : except the numbers 9, 14, 121, 329, 659, 4523, 7307 and 212533, a(n) is a Lucas number (A000204).

LINKS

Table of n, a(n) for n=1..34.

EXAMPLE

The non-Lucas number 9 is in the sequence because 9^2-1 = 80 = 2*5*8 is the product of three Fibonacci numbers.

The Lucas number 11 is in the sequence because 11^2-1 = 120 = 3*5*8 is the product of three Fibonacci numbers.

MAPLE

with(combinat, fibonacci):with(numtheory):nn:=150:lst:={}:T:=array(1..nn):

   for n from 1 to nn do:

    T[n]:=fibonacci(n):

   od:

     for p from 1 to nn-1 do:

       for q from p+1 to nn-1 do:

          for r from q+1 to nn-1 do:

           f:=T[p]*T[q]*T[r]+1:x:=sqrt(f):

           if x=floor(x)and T[p]<>1

           then

           lst:=lst union {x}:

           else

           fi:

          od:

       od:

     od:

     print(lst):

PROG

(PARI)

v=[]; for(i=3, 100, for(j=i+1, 100, for(k=j+1, 100, s=fibonacci(i)*fibonacci(j)*fibonacci(k); if(issquare(s+1), v=concat(sqrtint(s+1), v))))); v=vecsort(v); v \\ Derek Orr, Aug 27 2014

CROSSREFS

Cf. A245688, A242074, A000204.

Sequence in context: A267970 A024828 A139058 * A328454 A254937 A222947

Adjacent sequences:  A242100 A242101 A242102 * A242104 A242105 A242106

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 15 2014

STATUS

approved

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Last modified December 7 00:16 EST 2019. Contains 329812 sequences. (Running on oeis4.)