A110368 Integers with mutual residues of 9.

10, 19, 199, 37819, 1429936399, 2044718092315659619, 4180872077042990313463432060226288599, 17479691324597767931283328689425028720038746822457352536058485868000785419

Offset: 1

Author

Seppo Mustonen, Sep 04 2005

Keywords

• nonn

Comments

This is the special case k=9 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.

Links

• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437.
• A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437 (original plus references that F.Q. forgot to include - see last page!)
• Stanislav Drastich, Rapid growth sequences, arXiv:math/0202010 [math.GM], 2002.
• S. W. Golomb, On certain nonlinear recurring sequences, Amer. Math. Monthly 70 (1963), 403-405.
• S. Mustonen, On integer sequences with mutual k-residues
• Index entries for sequences of form a(n+1)=a(n)^2 + ....

Crossrefs

Column k=9 of A177888.

Programs

Mathematica

RecurrenceTable[{a[1]==10, a[n]==a[n-1]*(a[n-1]-9)+9}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 17 2014 *)

Formula

a(n) ~ c^(2^n), where c = 1.9324294501525084771045650938374200605001383645783351474944965038078432359... . - Vaclav Kotesovec, Dec 17 2014