A000289 A nonlinear recurrence: a(n) = a(n-1)^2 - 3*a(n-1) + 3 (for n>1). (Formerly M3316 N1333)

1, 4, 7, 31, 871, 756031, 571580604871, 326704387862983487112031, 106735757048926752040856495274871386126283608871, 11392521832807516835658052968328096177131218666695418950023483907701862019030266123104859068031

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, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, alternative link.

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