A332181 a(n) = 8*(10^(2n+1)-1)/9 - 7*10^n.

1, 818, 88188, 8881888, 888818888, 88888188888, 8888881888888, 888888818888888, 88888888188888888, 8888888881888888888, 888888888818888888888, 88888888888188888888888, 8888888888881888888888888, 888888888888818888888888888, 88888888888888188888888888888, 8888888888888881888888888888888

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. (A077776-1)/2 = A183184: indices of primes.

Cf. A002275 (repunits R_n = (10^n-1)/9), A002282 (8*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits only).

Cf. A332121 .. A332191 (variants with different repeated digit 2, ..., 9).

Cf. A332180 .. A332189 (variants with different middle digit 0, ..., 9).

Programs

Maple

A332181 := n -> 8*(10^(2*n+1)-1)/9-7*10^n;

Mathematica

Array[8 (10^(2 # + 1)-1)/9 - 7*10^# &, 15, 0]

PARI

apply( {A332181(n)=10^(n*2+1)\9*8-7*10^n}, [0..15])

Python

def A332181(n): return 10**(n*2+1)//9*8-7*10**n

Formula

a(n) = 8*A138148(n) + 10^n = A002282(2n+1) - 7*10^n.

G.f.: (1 + 707*x - 1500*x^2)/((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.