A332191 a(n) = 10^(2n+1) - 1 - 8*10^n.

1, 919, 99199, 9991999, 999919999, 99999199999, 9999991999999, 999999919999999, 99999999199999999, 9999999991999999999, 999999999919999999999, 99999999999199999999999, 9999999999991999999999999, 999999999999919999999999999, 99999999999999199999999999999, 9999999999999991999999999999999

Offset

0,2

Comments

See A183184 = {1, 5, 13, 43, 169, 181, ...} for the indices of primes.

Links

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

Patrick De Geest, Palindromic Wing Primes: (9)1(9), updated: June 25, 2017.

Makoto Kamada, Factorization of 9999199...99, updated Dec 11 2018.

Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

Formula

a(n) = 9*A138148(n) + 10^n.

G.f.: (1 + 808*x - 1700*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

A332191 := n -> 10^(n*2+1)-1-8*10^n;

Mathematica

Array[ 10^(2 # + 1)-1-8*10^# &, 15, 0]

Prog

(PARI) apply( {A332191(n)=10^(n*2+1)-1-8*10^n}, [0..15])
(Python) def A332191(n): return 10**(n*2+1)-1-8*10^n

Crossrefs

Cf. (A077776-1)/2 = A183184: 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. A332121 .. A332181 (variants with different repeated digit 2, ..., 8).

Cf. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).

Sequence in context: A162870 A251133 A083142 * A068163 A289794 A235881

Adjacent sequences: A332188 A332189 A332190 * A332192 A332193 A332194

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved