A240229 a(n) is the shortest concatenation of the Fibonacci numbers F(1), F(2), ..., divisible by F(n) = A000045(n), n >= 1. a(n) = 0 if there is no such concatenation.

1, 1, 112, 11235, 11235, 112, 1123581321345589144233, 11235, 11235813213455891442333776109871597258, 11235813213455891442333776109871597258441816765, 1123581321345589144233377610987159725844181676, 1123581321345589144233377610987159725844181676510946177112865746368

Offset: 1

Author

Wolfdieter Lang, May 10 2014

Keywords

• nonn
• base
• less

Comments

The corresponding numbers a(n)/F(n) are 1, 1, 56, 3745, 2247, 14, 86429332411199164941, 535, 330465094513408571833346356172694037, 204287512971925298951523201997665404698942123, 12624509228602125216105366415586064335327884, 7802648064899924612731788965188609207251261642437126229950456572, ...

The author's opinion is that this is an example of a not-so-interesting sequence. I call this a WOTS (waste of time sequence). But because I had to write a program to test similar proposed sequences I thought I would apply it to this prominent example.

The next entry a(13) has 324 digits for the divisibility by F(13) = 233 with a(13)/F(13) a 321 digit composite. The given a(n) are all nonprimes.

Question: is there an n with a(n) = 0?

Examples

			a(3) = 112 because neither 1 nor 11 are divisible by F(3) = 2, but 112, the concatenation of F(1), F(2) and F(3) is.
		

Crossrefs

Cf. A096098, A096097, A240588.

Formula

See the name.