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

0,1

Comments

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

Links

Table of n, a(n) for n=0..15.

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).

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.

Maple

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

Mathematica

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

Prog

(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

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).

Sequence in context: A318066 A216375 A157332 * A229203 A024072 A119549

Adjacent sequences: A332192 A332193 A332194 * A332196 A332197 A332198

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved