|
| |
|
|
A000289
|
|
A nonlinear recurrence: a(n) = a(n-1)^2 - 3*a(n-1) + 3 (for n>1).
(Formerly M3316 N1333)
|
|
11
|
|
|
|
1, 4, 7, 31, 871, 756031, 571580604871, 326704387862983487112031, 106735757048926752040856495274871386126283608871, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068031
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,2
|
|
|
COMMENTS
|
An infinite coprime sequence defined by recursion. - Michael Somos, Mar 14 2004
This is the special case k=3 of sequences with exact mutual k-residues. In general, a(1)=k+1 and a(n)=min{m | m>a(n-1), mod(m,a(i))=k, i=1,...,n-1}. k=1 gives Sylvester's sequence A000058 and k=2 Fermat sequence A000215. - Seppo Mustonen, Sep 04 2005
|
|
|
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..12
A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fib. Quart., 11 (1973), 429-437.
S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 70 (1963), 403-405.
R. Mestrovic, Euclid's theorem on the infinitude of primes: a historical survey of its proofs (300 BC--2012) and another new proof, arXiv preprint arXiv:1202.3670 [math.HO], 2012 - From N. J. A. Sloane, Jun 13 2012
S. Mustonen, On integer sequences with mutual k-residues
Seppo Mustonen, On integer sequences with mutual k-residues [Local copy]
Index entries for sequences of form a(n+1)=a(n)^2 + ...
|
|
|
FORMULA
|
a(n) = A005267(n) + 2 (for n>0).
a(n) = ceiling(c^(2^n)) + 1 where c = A077141. - Benoit Cloitre, Nov 29 2002
For n>0, a(n) = 3 + Product_{i=0..n-1} a(i). - Vladimir Shevelev, Dec 08 2010
|
|
|
MATHEMATICA
|
Join[{1}, RecurrenceTable[{a[n] == a[n-1]^2 - 3*a[n-1] + 3, a[1] == 4}, a, {n, 1, 9}]] (* Jean-François Alcover, Feb 06 2016 *)
|
|
|
PROG
|
(PARI) a(n)=if(n<2, max(0, 1+3*n), a(n-1)^2-3*a(n-1)+3)
|
|
|
CROSSREFS
|
Cf. A000058.
Sequence in context: A156228 A218959 A283332 * A241426 A271676 A149089
Adjacent sequences: A000286 A000287 A000288 * A000290 A000291 A000292
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
STATUS
|
approved
|
| |
|
|
