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

Author

M. F. Hasler, Feb 08 2020

Keywords

• nonn
• base
• easy

Comments

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

Links

• 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).

Crossrefs

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).

Programs

Maple

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

Mathematica

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

PARI

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

Python

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

Formula

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.