A332179 a(n) = 7*(10^(2n+1)-1)/9 + 2*10^n.

9, 797, 77977, 7779777, 777797777, 77777977777, 7777779777777, 777777797777777, 77777777977777777, 7777777779777777777, 777777777797777777777, 77777777777977777777777, 7777777777779777777777777, 777777777777797777777777777, 77777777777777977777777777777, 7777777777777779777777777777777

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Comments

See A183183 = {1, 2, 8, 19, 20, 212, 280, ...} 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. (A077796-1)/2 = A183183: indices of primes.

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

Cf. A332171 .. A332178 (variants with different middle digit 1, ..., 8).

Programs

Maple

A332179 := n -> 7*(10^(n*2+1)-1)/9 + 2*10^n;

Mathematica

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

PARI

apply( {A332179(n)=10^(n*2+1)\9*7+2*10^n}, [0..15])

Python

def A332179(n): return 10**(n*2+1)//9*7+2*10^n

Formula

a(n) = 7*A138148(n) + 9*10^n.

G.f.: (9 - 202*x - 500*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.