A332175 a(n) = 7*(10^(2n+1)-1)/9 - 2*10^n.

5, 757, 77577, 7775777, 777757777, 77777577777, 7777775777777, 777777757777777, 77777777577777777, 7777777775777777777, 777777777757777777777, 77777777777577777777777, 7777777777775777777777777, 777777777777757777777777777, 77777777777777577777777777777, 7777777777777775777777777777777

Offset: 0

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Comments

See A183180 = {0, 1, 7, 13, 58, 129, 253, ...} for the indices of primes.

Links

• Makoto Kamada, Factorization of 77...77577...77, updated Dec 11 2018.
• Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Crossrefs

Cf. (A077785-1)/2 = A183180: indices of primes.

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

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

A332175 := 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( {A332175(n)=10^(n*2+1)\9*7-2*10^n}, [0..15])

Python

def A332175(n): return 10**(n*2+1)//9*7-2*10^n

Formula

a(n) = 7*A138148(n) + 5*10^n.

G.f.: (5 + 202*x - 900*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) - 18*exp(9*x) - 7). - Stefano Spezia, Feb 08 2020