A332112 a(n) = (10^(2n+1)-1)/9 + 10^n.

2, 121, 11211, 1112111, 111121111, 11111211111, 1111112111111, 111111121111111, 11111111211111111, 1111111112111111111, 111111111121111111111, 11111111111211111111111, 1111111111112111111111111, 111111111111121111111111111, 11111111111111211111111111111, 1111111111111112111111111111111

Offset

0,1

Comments

a(0) = 2 is the only prime in this sequence, since all other terms factor as a(n) = R(n+1)*(10^n+1), where R(n) = (10^n-1)/9.

Links

Table of n, a(n) for n=0..15.

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

Formula

a(n) = A138148(n) + 2*10^n = A002275(2n+1) + 10^n.

G.f.: (2 - 101*x)/((1 - x)(1 - 10*x)(1 - 100*x)).

a(n) = 111*a(n-1) - 1110*a(n-2) + 1000*a(n-3) for n > 2.

Maple

A332112 := n -> (10^(2*n+1)-1)/9+10^n;

Mathematica

Array[ (10^(2 # + 1)-1)/9 + 10^# &, 15, 0]

Prog

(PARI) apply( {A332112(n)=10^(n*2+1)\9*1+10^n}, [0..15])
(Python) def A332112(n): return 10**(n*2+1)//9+10**n

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332132 .. A332192 (variants with different repeated digit 3, ..., 9).

Cf. A332113 .. A332119 (variants with different middle digit 3, ..., 9).

Cf. A331860 & A331861 (indices of primes in non-palindromic variants).

Sequence in context: A042799 A281983 A217023 * A074490 A056638 A222873

Adjacent sequences: A332109 A332110 A332111 * A332113 A332114 A332115

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved