A001543 a(0) = 1, a(n) = 5 + Product_{i=0..n-1} a(i) for n > 0. (Formerly M4091 N1699)

1, 6, 11, 71, 4691, 21982031, 483209576974811, 233491495280173380882643611671, 54518278368171228201482876236565907627201914279213829353891

Offset

0,2

Comments

This is the special case k=5 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

Alois P. Heinz, 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. - 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) = a(n-1) * (a(n-1) - 5) + 5. - Charles R Greathouse IV, Dec 09 2011

a(n) ~ c^(2^n), where c = 1.696053774403103324180661918166106455311376345474042496749974632237971081462... . - Vaclav Kotesovec, Dec 17 2014

Mathematica

Flatten[{1, RecurrenceTable[{a[1]==6, a[n]==a[n-1]*(a[n-1]-5)+5}, a, {n, 1, 10}]}] (* Vaclav Kotesovec, Dec 17 2014 *)
Join[{1}, NestList[#(#-5)+5&, 6, 10]] (* Harvey P. Dale, Oct 10 2016 *)

Prog

(PARI) {
  print1("1, 6");
  n=6;
  m=Mod(5, 6);
  for(i=2, 9,
    n=m.mod+lift(m);
    m=chinese(m, Mod(5, n));
    print1(", "n)
  )
} \\ Charles R Greathouse IV, Dec 09 2011

Crossrefs

Column k=5 of A177888.

Sequence in context: A061519 A193664 A080875 * A077705 A077697 A283820

Adjacent sequences: A001540 A001541 A001542 * A001544 A001545 A001546

Keyword

nonn

Author

N. J. A. Sloane.

Extensions

New name from Alonso del Arte, Dec 09 2011

Status

approved