A332174 a(n) = 7*(10^(2n+1)-1)/9 - 3*10^n.

4, 747, 77477, 7774777, 777747777, 77777477777, 7777774777777, 777777747777777, 77777777477777777, 7777777774777777777, 777777777747777777777, 77777777777477777777777, 7777777777774777777777777, 777777777777747777777777777, 77777777777777477777777777777, 7777777777777774777777777777777

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Comments

See A183179 = {2, 3, 6, 23, 36, 69, 561, ...} for the indices of primes.

Links

• Makoto Kamada, Factorization of 77...77477...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. (A077781-1)/2 = A183179: 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

A332174 := n -> 7*(10^(n*2+1)-1)/9 - 3*10^n;

Mathematica

Array[7 (10^(2 # + 1) - 1)/9 - 3*10^# &, 15, 0]

PARI

apply( {A332174(n)=10^(n*2+1)\9*7-3*10^n}, [0..15])

Python

def A332174(n): return 10**(n*2+1)//9*7-3*10^n

Formula

a(n) = 7*A138148(n) + 4*10^n.

G.f.: (4 + 303*x - 1000*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.

E.g.f.: (1/9)*exp(x)*(70*exp(99*x) - 27*exp(9*x) - 7). - Stefano Spezia, Feb 08 2020