A332197 a(n) = 10^(2n+1) - 1 - 2*10^n.

7, 979, 99799, 9997999, 999979999, 99999799999, 9999997999999, 999999979999999, 99999999799999999, 9999999997999999999, 999999999979999999999, 99999999999799999999999, 9999999999997999999999999, 999999999999979999999999999, 99999999999999799999999999999, 9999999999999997999999999999999

Offset

0,1

Comments

According to Kamada, n = 118 and n = 145126 are the only known indices of primes (the so-called palindromic near-repdigit or wing primes).

Links

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

Patrick De Geest, Palindromic Wing Primes: (9)7(9), updated June 25, 2017.

Makoto Kamada, Factorization of 99...99799...99, updated Dec 11 2018.

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

Formula

a(n) = 9*A138148(n) + 7*10^n.

G.f.: (7 + 202*x - 1100*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

A332197 := n -> 10^(n*2+1)-1-2*10^n;

Mathematica

Array[ 10^(2 # + 1) -1 -2*10^# &, 15, 0]
Table[FromDigits[Join[PadRight[{}, n, 9], {7}, PadRight[{}, n, 9]]], {n, 0, 20}] (* or *) LinearRecurrence[{111, -1110, 1000}, {7, 979, 99799}, 20] (* Harvey P. Dale, Mar 03 2023 *)

Prog

(PARI) apply( {A332197(n)=10^(n*2+1)-1-2*10^n}, [0..15])
(Python) def A332197(n): return 10**(n*2+1)-1-2*10^n

Crossrefs

Cf. A002275 (repunits R_n = (10^n-1)/9), A002283 (9*R_n), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits only).

Cf. A332190 .. A332196, A181965 (variants with different middle digit 0, ..., 8).

Cf. A332117 .. A332187 (variants with different repeated digit 1, ..., 9).

Sequence in context: A172918 A286913 A201070 * A213960 A173852 A062841

Adjacent sequences: A332194 A332195 A332196 * A332198 A332199 A332200

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 08 2020

Status

approved