A344423 a(n) = 10^(2*n+2) + 111*10^n + 1.

212, 11111, 1011101, 100111001, 10001110001, 1000011100001, 100000111000001, 10000001110000001, 1000000011100000001, 100000000111000000001, 10000000001110000000001, 1000000000011100000000001, 100000000000111000000000001, 10000000000001110000000000001

Offset: 0

Author

Felix Fröhlich, May 18 2021

Keywords

• nonn
• easy

Comments

For n > 1, palindromic numbers of the form 10..01110..01.

This is the earliest sequence of the form 10^(2*n+t) + A002275(t+1)*10^n + 1 that contains primes of the form mentioned in the previous comment. For example, the terms of the sequence for t = 0 are all divisible by 3 (see A066138, where 3 is the only prime), while each term b(i) of the sequence with t = 1 (A319667) is divisible by 10^i+1.

For the values of n such that a(n) is prime, see A344424.

Links

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

Crossrefs

Cf. A002275, A066138, A319667, A344424.

Programs

PARI

a(n) = 10^(2*n+2) + 111*10^n + 1

Formula

G.f.: -(13100*x^2 - 12421*x + 212)/(1000*x^3 - 1110*x^2 + 111*x - 1). - Jinyuan Wang, May 22 2021

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3). - Wesley Ivan Hurt, May 22 2021

E.g.f.: exp(x)*(1 + 111*exp(9*x) + 100*exp(99*x)). - Stefano Spezia, May 22 2021