A049998

[Ralf Stephan]

Dean Hickerson:
> > Conjecture:
> > Differences of products F(k)F(l)F(m), regardless of order,
> > are either Fibonacci numbers, Lucas numbers, or products of both.
> 
> No, 1375 = 5*5*55 and 1398 = 2*3*233 are consecutive products of 3 Fibonaccis,
> but their difference, 23, is not a product of Fibonacci and Lucas numbers.

Right. The pattern of hits starts

1111111111111111110111110110111011101110101101110101110111010110101110101110
1011101010110101110101011101011101010110101011101010111010101110101010110101
0111010101011101010111010101011010101011101010101110101010111010101010110101
0101110101010101110101010111010101010110101010101110101010101110101010101110
1010101010110101010101110101010101011101010101011101010101010110101010101011
1010101010101110101010101011101010101010101101010101010111010101010101011101
0101010101110101010101010110101010101010111010101010101011101010101010101110
...

so the conjecture appears true for only half of the cases.
The numbers that don't hit the pattern start

23,37,41,60,66,97,103,107,157,167,173,254,270,274,280,411,437,443,453,665,707,
713,717,733,1076,1144,1154,1160,1186,1741,1851,1867,1871,1877,1919,2817,2995,
3021,3027,3037,3105,4558,4846,4888,4894,4898,4914,5024,7375,7841,7909,7919,
7925,7951,8129,11933,12687,12797,12813,12817,12823,12865,13153,19308,20528,
20706,20732,20738,20748,20816,21282,31241,33215,33503,33545,33551,33555,33571,
33681,34435,50549,53743,54209,54277,54287,54293,54319,54497,55717,81790,86958,
87712,87822,87838,87842,87848,87890,88178,90152,132339,140701,141921,142099,


ralf