login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001696 a(n) = a(n-1)*(1 + a(n-1) - a(n-2)), a(0) = 0, a(1) = 1.
(Formerly M1268 N0487)
4
0, 1, 2, 4, 12, 108, 10476, 108625644, 11798392680793836, 139202068568601568785946949658348, 19377215893777651167043206536157529523359277782016064519251404524 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also, numbers remaining after the following sieving process: In step 1, keep all numbers of the set N={0,1,2,...}. In step 2, keep only every second number after a(2)=2: N'={0,1,2,4,6,8,10,...}. In step 3, keep every 4th of the numbers following a(3)=4, N"={0,1,2,4,12,20,28,...}. In step 4, keep every 12th of the numbers beyond a(4)=12: {0,1,2,4,12,108,204,...}. In step 5, keep every 108th of the numbers beyond a(5)=108: {0,1,2,4,12,108,10476,...}, and so on. The next "gap" a(n+1)-a(n) is always a(n) times the former gap, i.e., a(n+1)-a(n) = a(n)*(a(n)-a(n-1)). [From M. F. Hasler, Oct 28 2010]

REFERENCES

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

John Cerkan, Table of n, a(n) for n = 0..13

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.

Index entries for sequences of form a(n+1)=a(n)^2 + ...

FORMULA

a(n) ~ c^(2^n), where c =

1.15552822483840350150537253088299651035583896919522349372370013726451673646... . - Vaclav Kotesovec, May 21 2015

MATHEMATICA

a[0] = 0; a[1] = 1; a[n_] := a[n] = a[n-1]*(1 + a[n-1] - a[n-2]); Table[a[n], {n, 0, 10}] (* Jean-Fran├žois Alcover, Jul 02 2013 *)

PROG

(PARI) a(n)=if(n<2, n>0, a(n-1)*(1+a(n-1)-a(n-2)))

(Haskell)

a001696 n = a001696_list !! n

a001696_list = 0 : 1 : zipWith (-)

   (zipWith (+) a001696_list' $ map (^ 2) a001696_list')

   (zipWith (*) a001696_list a001696_list')

   where a001696_list' = tail a001696_list

-- Reinhard Zumkeller, Apr 29 2013

CROSSREFS

a(n)=A039941(2*n); first difference sequence of this sequence is A001697. - Michael Somos, May 19 2000

Sequence in context: A228809 A230814 A038791 * A276534 A304986 A013333

Adjacent sequences:  A001693 A001694 A001695 * A001697 A001698 A001699

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 12:34 EDT 2018. Contains 316379 sequences. (Running on oeis4.)