A332172 a(n) = 7*(10^(2n+1)-1)/9 - 5*10^n.

2, 727, 77277, 7772777, 777727777, 77777277777, 7777772777777, 777777727777777, 77777777277777777, 7777777772777777777, 777777777727777777777, 77777777777277777777777, 7777777777772777777777777, 777777777777727777777777777, 77777777777777277777777777777, 7777777777777772777777777777777

Offset: 0

Author

M. F. Hasler, Feb 06 2020

Keywords

• nonn
• base
• easy

Comments

Indices of prime terms: {0, 1, 3, 7, 10, 12, 480, 949, ...} = A183178.

Links

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

Crossrefs

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

Cf. A332171 (analog with middle digit 1).

Cf. (A077777-1)/2 = A183178: indices of primes.

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

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

Programs

Maple

A332172 := n -> 7*(10^(n*2+1)-1)/9 -5*10^n;

Mathematica

Array[7 (10^(2 # +1)-1)/9 -5*10^# &, 15, 0]

PARI

apply( {A332172(n)=10^(n*2+1)\9*7-5*10^n}, [0..25])

Python

def A332172(n): return 10**(n*2+1)//9*7-5*10^n

Formula

a(n) = 7*A138148(n) + 2*10^n.

G.f.: (2 + 505*x - 1200*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.