A098608 a(n) = 100^n.

1, 100, 10000, 1000000, 100000000, 10000000000, 1000000000000, 100000000000000, 10000000000000000, 1000000000000000000, 100000000000000000000, 10000000000000000000000, 1000000000000000000000000, 100000000000000000000000000, 10000000000000000000000000000, 1000000000000000000000000000000

Offset: 0

Author

Henry Bottomley, Sep 17 2004

Keywords

• easy
• nonn

Comments

For any base B, these are the numbers (B^2)^n written in base B. - Philippe Deléham, Jan 06 2008

Conjecture: a(n) are the only positive squares (in base 10) with digits in {0,1}. - Manfred Boergens, Feb 10 2025

References

• Stephen Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Links

• Tanya Khovanova, Recursive Sequences.
• Robert Price, Comments on A098608 concerning Elementary Cellular Automata, Feb 20 2016.
• Stephen Wolfram, A New Kind of Science
• Index entries for linear recurrences with constant coefficients, signature (100).
• Index to Elementary Cellular Automata
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A011557, A098609.

Programs

Mathematica

LinearRecurrence[{100},{1},12] (* Ray Chandler, Aug 17 2015 *)
NestList[100#&,1,20] (* Harvey P. Dale, Dec 28 2018 *)

Formula

a(n) = 100*a(n-1) = A011557(2n) = A098609(n) + 1.

G.f.: 1/(1-100x).

E.g.f.: exp(100*x). - Stefano Spezia, Aug 05 2024

Extensions

a(12)-a(15) from Stefano Spezia, Aug 05 2024