

A344423


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


1



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

0,1


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

Table of n, a(n) for n=0..13.
Index entries for linear recurrences with constant coefficients, signature (111,1110,1000).


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(n1)  1110*a(n2) + 1000*a(n3).  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


PROG

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


CROSSREFS

Cf. A002275, A066138, A319667, A344424.
Sequence in context: A254704 A267062 A250326 * A238023 A204299 A332121
Adjacent sequences: A344420 A344421 A344422 * A344424 A344425 A344426


KEYWORD

nonn,easy


AUTHOR

Felix FrÃ¶hlich, May 18 2021


STATUS

approved



