A183186 -id:A183186 - cp's OEIS frontend

A332195 a(n) = 10^(2n+1) - 4*10^n - 1.

5, 959, 99599, 9995999, 999959999, 99999599999, 9999995999999, 999999959999999, 99999999599999999, 9999999995999999999, 999999999959999999999, 99999999999599999999999, 9999999999995999999999999, 999999999999959999999999999, 99999999999999599999999999999, 9999999999999995999999999999999

Offset: 0

M. F. Hasler, Feb 08 2020

See A183186 = {88, 112, 198, 622, 4228, ...} for the indices of primes.

Patrick De Geest, Palindromic Wing Primes: (9)5(9), updated Jun 25 2017.
Makoto Kamada, Factorization of 99...99599...99, updated Dec 11 2018.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Cf. (A077786-1)/2 = A183186: 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. A332115 .. A332185 (variants with different repeated digit 1, ..., 8).
Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).

Maple
```
A332195 := n -> 10^(n*2+1)-4*10^n-1;
```

Array[ 10^(2 # + 1) - 1 - 4*10^# &, 15, 0]

apply( {A332195(n)=10^(n*2+1)-1-4*10^n}, [0..15])

def A332195(n): return 10**(n*2+1)-1-4*10^n

a(n) = 9*A138148(n) + 5*10^n.
G.f.: (5 + 404*x - 1300*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.

A077786 Numbers k such that (10^k - 1) - 4*10^floor(k/2) is a palindromic wing prime (a.k.a. near-repdigit palindromic prime).

Original entry on oeis.org

177, 225, 397, 1245, 8457, 20105, 111725

Offset: 1

Patrick De Geest, Nov 16 2002

Prime versus probable prime status and proofs are given in the author's table.

			177 is a term because (10^177 - 1) - 4*10^88 = 99...99599...99.

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...99599...99
Index entries for primes involving repunits.

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

Do[ If[ PrimeQ[10^n - 4*10^Floor[n/2] - 1], Print[n]], {n, 3, 20200, 2}] (* Robert G. Wilson v, Dec 16 2005 *)

a(n) = 2*A183186(n) + 1.

One more term from PWP table added by Patrick De Geest, Nov 05 2014

Name corrected by Jon E. Schoenfield, Oct 31 2018

cp's OEIS Frontend

A332195 a(n) = 10^(2n+1) - 4*10^n - 1.

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