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

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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 + ...

Crossrefs

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

Programs

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 *)

PARI

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

Formula

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