This site is supported by donations to The OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A001543 a(0) = 1, a(n) = 5 + Product_{i=0..n-1} a(i) for n > 0. (Formerly M4091 N1699) 5
 1, 6, 11, 71, 4691, 21982031, 483209576974811, 233491495280173380882643611671, 54518278368171228201482876236565907627201914279213829353891 (list; graph; refs; listen; history; text; internal format)
 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, Fib. Quart., 11 (1973), 429-437. 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 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==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 EXTENSIONS New name from Alonso del Arte, Dec 09 2011 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified July 20 23:29 EDT 2019. Contains 325189 sequences. (Running on oeis4.)