A332176 a(n) = 7*(10^(2n+1)-1)/9 - 10^n.

6, 767, 77677, 7776777, 777767777, 77777677777, 7777776777777, 777777767777777, 77777777677777777, 7777777776777777777, 777777777767777777777, 77777777777677777777777, 7777777777776777777777777, 777777777777767777777777777, 77777777777777677777777777777, 7777777777777776777777777777777

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Comments

See A183181 = {4, 5, 8, 11, 1244, 1685, ...} for the indices of primes.

Links

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

Crossrefs

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

Cf. (A077788-1)/2 = A183181: indices of primes.

Cf. A002275 (repunits R_n = (10^n-1)/9), A002281 (7*R_n), A011557 (10^n).

Cf. A332171 .. A332179 (variants with different middle digit 1, ..., 9).

Programs

Maple

A332176 := n -> 7*(10^(n*2+1)-1)/9 - 10^n;

Mathematica

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

PARI

apply( {A332176(n)=10^(n*2+1)\9*7-10^n}, [0..15])

Python

def A332176(n): return 10**(n*2+1)//9*7-10^n

Formula

a(n) = 7*A138148(n) + 6*10^n.

G.f.: (6 + 101*x - 800*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.