A077782 -id:A077782 - cp's OEIS frontend

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

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.

A183185 Numbers n such that 10^(2n+1)-5*10^n-1 is prime.

Original entry on oeis.org

14, 22, 36, 104, 1136, 17864, 25448

Offset: 1

Ray Chandler, Dec 28 2010

C. Caldwell and H. Dubner, "Journal of Recreational Mathematics", Volume 28, No. 1, 1996-97, pp. 1-9.

Patrick De Geest, World!Of Numbers, Palindromic Wing Primes (PWP's)
Makoto Kamada, Prime numbers of the form 99...99499...99
Index entries for primes involving repunits.

Cf. A004023, A077775-A077798, A107123-A107127, A107648, A107649, A115073, A183174-A183187.

Do[If[PrimeQ[10^(2n + 1) - 5*10^n - 1], Print[n]], {n, 3000}]

is(n)=ispseudoprime(10^(2*n+1)-5*10^n-1) \\ Charles R Greathouse IV, Jun 13 2017

a(n) = (A077782(n)-1)/2.

cp's OEIS Frontend

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

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