A332184 -id:A332184 - cp's OEIS frontend

4, 949, 99499, 9994999, 999949999, 99999499999, 9999994999999, 999999949999999, 99999999499999999, 9999999994999999999, 999999999949999999999, 99999999999499999999999, 9999999999994999999999999, 999999999999949999999999999, 99999999999999499999999999999, 9999999999999994999999999999999

Offset: 0

M. F. Hasler, Feb 08 2020

See A183185 = {14, 22, 36, 104, 1136, ...} for the indices of primes.

Patrick De Geest, Palindromic Wing Primes: (9)4(9), updated Jun 25 2017.
Makoto Kamada, Factorization of 99...99499...99, updated Dec 11 2018.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. (A077782-1)/2 = A183185: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits only), A002113 (palindromes).
Cf. A332114 .. A332184 (variants with different repeated digit 1, ..., 8).
Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).

Maple
```
A332194 := n -> 10^(n*2+1)-1-5*10^n;
```

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

apply( {A332194(n)=10^(n*2+1)-1-5*10^n}, [0..15])

def A332194(n): return 10**(n*2+1)-1-5*10^n

a(n) = 9*A138148(n) + 4*10^n = A002283(2n+1) - 5*A011557(n).
G.f.: (4 + 505*x - 1400*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.

cp's OEIS Frontend

A332194 a(n) = 10^(2n+1) - 1 - 5*10^n.

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