A332178 a(n) = 7*(10^(2n+1)-1)/9 + 10^n.

8, 787, 77877, 7778777, 777787777, 77777877777, 7777778777777, 777777787777777, 77777777877777777, 7777777778777777777, 777777777787777777777, 77777777777877777777777, 7777777777778777777777777, 777777777777787777777777777, 77777777777777877777777777777, 7777777777777778777777777777777

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Comments

See A183182 = {1, 3, 39, 54, 168, 240, ...} for the indices of primes.

Links

• Makoto Kamada, Factorization of 77...77877...77, updated Dec 11 2018.
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

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

Cf. (A077793-1)/2 = A183182: 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

A332178 := n -> 7*(10^(n*2+1)-1)/9 + 10^n;

Mathematica

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

PARI

apply( {A332178(n)=10^(n*2+1)\9*7+10^n}, [0..15])

Python

def A332178(n): return 10**(n*2+1)//9*7+10^n

Formula

a(n) = 7*A138148(n) + 8*10^n.

G.f.: (8 - 101*x - 600*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.