# Fibs

N. J. A. Sloane njas at research.att.com
Mon Jan 24 00:23:22 CET 2000

```Responding to john conway's comments:

If you enter
1 1 2 3 5 8 13 21 34 55 89 144 233 377
the Fibonacci numbers are the 4th matching sequence

There's now a button whereby you can control how
many matching sequences you want to see (just as with Math Review
lookups)

I agree there are too many dull sequences in the table,

On the other hand you should see the ones i do reject!

Here are a couple you will be glad i did not reject, taken just from
the last couple of days' arrivals:

%I A052109
%S A052109 1,1,2,5,12,30,73,178,434,1058,2580,6291,15341,37408,91217,222427,
%T A052109 542374
%N A052109 a(1)=1, a(n)=a(n-a(1))+a(n-a(2))+a(n-a(3))+....a(n-a(n-1)) for n>1, with convention that a(i)=0 for i<=0.
%e A052109 a(5)=a(4)+a(4)+a(3)=5+5+2=12.
%O A052109 1,3
%K A052109 easy,nonn,nice,more
%A A052109 Robert Lozyniak (rampshot at usa.net), Jan 20 2000

%I A052130
%S A052130 1,2,7,15,37,84,187,421,914,2001,4283,9184
%N A052130 For m very large, a(n) = number of numbers between 1 and 2^m with m-n prime factors (counted with multiplicity).
%e A052130 Between 1 and 2^m there is just one number with m prime factor, namely 2^m, so a(0) = 1. There are 2 numbers with m-1 prime factors (2^(m-1) and 3*2^(m-2)), so a(1) = 2.
%O A052130 0,2
%K A052130 nonn,nice,more
%A A052130 Bernd-Rainer Lauber (br.lauber at surf1.de), Jan 21 2000

Cute, don't you agree?

NJAS

```