A001544 A nonlinear recurrence: a(n) = a(n-1)^2 - 6*a(n-1) + 6, with a(0) = 1, a(1) = 7. (Formerly M4346 N1820)

1, 7, 13, 97, 8833, 77968897, 6079148431583233, 36956045653220845240164417232897, 1365749310322943329964576677590044473746108255675592519835615233

Offset

0,2

Comments

This is the special case k=6 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

Indranil Ghosh, Table of n, a(n) for n = 0..11

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. - N. J. A. Sloane, Jun 13 2012

Seppo 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) ~ c^(2^n), where c = 1.76450357631319101484804524709844019487003729926754942591419313922841785792... . - Vaclav Kotesovec, Dec 17 2014

Mathematica

Flatten[{1, RecurrenceTable[{a[1]==7, a[n]==a[n-1]*(a[n-1]-6)+6}, a, {n, 1, 10}]}] (* Vaclav Kotesovec, Dec 17 2014 *)
Join[{1}, NestList[#^2-6#+6&, 7, 10]] (* Harvey P. Dale, Nov 19 2024 *)

Prog

(PARI) a(n)=if(n<1, n==0, if(n==1, 7, n=a(n-1); n^2-6*n+6))

Crossrefs

Column k=6 of A177888. - Alois P. Heinz, Nov 07 2012

Sequence in context: A110293 A253333 A039687 * A202152 A136720 A323468

Adjacent sequences: A001541 A001542 A001543 * A001545 A001546 A001547

Keyword

nonn,changed

Author

N. J. A. Sloane

Status

approved