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]
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
New name from Alonso del Arte, Dec 09 2011
STATUS
approved