A332192 - OEIS

A332192

a(n) = 10^(2*n+1) - 1 - 7*10^n.

2, 929, 99299, 9992999, 999929999, 99999299999, 9999992999999, 999999929999999, 99999999299999999, 9999999992999999999, 999999999929999999999, 99999999999299999999999, 9999999999992999999999999, 999999999999929999999999999, 99999999999999299999999999999, 9999999999999992999999999999999

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OFFSET

0,1

COMMENTS

See A115073 = {1, 8, 9, 352, 530, 697, ...} for the indices of primes.

LINKS

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

Patrick De Geest, Palindromic Wing Primes: (9)2(9), updated: June 25, 2017.

Makoto Kamada, Factorization of 99...99299...99, updated Dec 11 2018.

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

FORMULA

a(n) = 9*A138148(n) + 2*10^n = A002283(2*n+1) - 7*10^n.

G.f.: (2 + 707*x - 1600*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.

E.g.f.: exp(x)*(10*exp(99*x) - 7*exp(9*x) - 1). - Elmo R. Oliveira, Dec 16 2025

MAPLE

A332192 := n -> 10^(n*2+1)-1-7*10^n;

MATHEMATICA

Array[ 10^(2 # +1) -1 -7*10^# &, 15, 0]

LinearRecurrence[{111, -1110, 1000}, {2, 929, 99299}, 20] (* Harvey P. Dale, Nov 07 2022 *)

Table[With[{c=PadRight[{}, n, 9]}, FromDigits[Join[c, {2}, c]]], {n, 0, 15}] (* Harvey P. Dale, Dec 13 2025 *)

PROG

(PARI) apply( {A332192(n)=10^(n*2+1)-1-7*10^n}, [0..15])

(Python) def A332192(n): return 10**(n*2+1)-1-7*10^n

CROSSREFS

Cf. (A077778-1)/2 = A115073: 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. A332190 .. A332197, A181965 (variants with different middle digit 0, ..., 8).

Cf. A332112 .. A332182 (variants with different repeated digit 1, ..., 8).

Sequence in context: A070967 A070927 A070922 * A258586 A176940 A389388

Adjacent sequences: A332189 A332190 A332191 * A332193 A332194 A332195

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Feb 08 2020

STATUS

approved