A110383 Integers with mutual residues of 10.

11, 21, 241, 55681, 3099816961, 9608865160705105921, 92330289676612360941221747472778199041, 8524882391767151111154918892947398067446166736305624023874497267723631329281

Offset

1,1

Comments

This is the special case k=10 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

Table of n, a(n) for n=1..8.

A. V. Aho and N. J. A. Sloane, Some doubly exponential sequences, Fibonacci Quarterly, Vol. 11, No. 4 (1973), pp. 429-437, alternative link.

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 + ....

Formula

a(n) ~ c^(2^n), where c = 1.9797221926746931491020959969764290497942241392143973226882604062455515473... . - Vaclav Kotesovec, Dec 17 2014

Mathematica

RecurrenceTable[{a[1]==11, a[n]==a[n-1]*(a[n-1]-10)+10}, a, {n, 1, 10}] (* Vaclav Kotesovec, Dec 17 2014 *)

Crossrefs

Column k=10 of A177888.

Sequence in context: A254208 A083177 A110466 * A123783 A163288 A092806

Adjacent sequences: A110380 A110381 A110382 * A110384 A110385 A110386

Keyword

nonn

Author

Seppo Mustonen, Sep 04 2005

Status

approved