A102807 a(n) is the square of one plus the number consisting of n 3's.

1, 16, 1156, 111556, 11115556, 1111155556, 111111555556, 11111115555556, 1111111155555556, 111111111555555556, 11111111115555555556, 1111111111155555555556, 111111111111555555555556, 11111111111115555555555556, 1111111111111155555555555556, 111111111111111555555555555556

Offset

0,2

Comments

Old name was: The number (333...334)^2.

An infinite sequence of squares with no zeros in base 10.

a(n) = A104265(2n) for n > 0. - Chai Wah Wu, Mar 24 2020

References

Albert H. Beiler, Recreations in the theory of numbers, New York, Dover, (2nd ed.) 1966. See Table 31 at p. 61.

Italo Ghersi, Matematica dilettevole e curiosa, pp. 111-112, Hoepli, Milano, 1967. [Vincenzo Librandi, Dec 31 2008]

Links

Seiichi Manyama, Table of n, a(n) for n = 0..500

Emile Fourrey, Récréations arithmétiques, Vuibert, 1899 and after, Paris, pages 72-73.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

From R. J. Mathar, Jan 06 2009: (Start)

a(n) = (100^n + 4*10^n + 4)/9.

G.f.: (1 - 95*x + 490*x^2)/((1-x)*(100*x-1)*(10*x-1)). (End)

E.g.f.: exp(x)*(4 + 4*exp(9*x) + exp(99*x))/9. - Stefano Spezia, Jul 31 2024

Maple

a:= n-> (1+parse(cat(0, 3$n)))^2:
seq(a(n), n=0..20);  # Alois P. Heinz, Sep 03 2018

Mathematica

Table[(10^n + 2)^2/9, {n, 0, 20}] (* Paolo Xausa, Jun 26 2024 *)

Crossrefs

Cf. A052041, A093137, A075415, A109344, A104265.

Sequence in context: A353029 A053903 A254333 * A373453 A160131 A206691

Adjacent sequences: A102804 A102805 A102806 * A102808 A102809 A102810

Keyword

nonn,base,easy

Author

Ron Knott, Feb 27 2005

Extensions

New name from Alois P. Heinz, Sep 03 2018

Status

approved