A031982 a(n) = 1(01)^(2*n+1).

101, 1010101, 10101010101, 101010101010101, 1010101010101010101, 10101010101010101010101, 101010101010101010101010101, 1010101010101010101010101010101, 10101010101010101010101010101010101, 101010101010101010101010101010101010101, 1010101010101010101010101010101010101010101

Offset: 0

Author

J. Castillo (arp(AT)cia-g.com)

Keywords

• nonn
• easy

References

• C. Ashbacher, Problem 514, The Pentagon, Vol. 57, No. 1, Fall 1997, p. 36.
• M. Le, On Smarandache Pierce Chain, Smarandache Notions Journal, Vol. 10, No. 1-2-3, 1999, pp. 154-155.
• Florentin Smarandache, Properties of the numbers, ASU Special Collections, 1973.

Links

• Eric Weisstein's World of Mathematics, Smarandache Sequences.
• Index entries for linear recurrences with constant coefficients, signature (10001,-10000).

Programs

Mathematica

101(10^(4Range[10]) - 1)/9999 (* Alonso del Arte, May 20 2017 *)
LinearRecurrence[{10001,-10000},{101,1010101},20] (* Harvey P. Dale, Aug 18 2019 *)

PARI

my(x='x+O('x^11)); Vec(101/((1-x)*(1-10000*x))) \\ Elmo R. Oliveira, Jun 12 2025

Formula

a(n) = 101*(10^(4*n) - 1)/(10^4 - 1).

From Elmo R. Oliveira, Jun 12 2025: (Start)

G.f.: 101/((x-1)*(10000*x-1)).

E.g.f.: 101*exp(x)*(exp(9999*x) - 1)/9999.

a(n) = 10001*a(n-1) - 10000*a(n-2). (End)

Extensions

More terms from James Sellers

a(9)-a(10) from Elmo R. Oliveira, Jun 12 2025