A332194 - OEIS

A332194

a(n) = 10^(2*n+1) - 1 - 5*10^n.

4, 949, 99499, 9994999, 999949999, 99999499999, 9999994999999, 999999949999999, 99999999499999999, 9999999994999999999, 999999999949999999999, 99999999999499999999999, 9999999999994999999999999, 999999999999949999999999999, 99999999999999499999999999999, 9999999999999994999999999999999

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OFFSET

0,1

COMMENTS

See A183185 = {14, 22, 36, 104, 1136, ...} for the indices of primes.

LINKS

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

Patrick De Geest, Palindromic Wing Primes: (9)4(9), updated Jun 25 2017.

Makoto Kamada, Factorization of 99...99499...99, updated Dec 11 2018.

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

FORMULA

a(n) = 9*A138148(n) + 4*10^n = A002283(2*n+1) - 5*A011557(n).

G.f.: (4 + 505*x - 1400*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) - 5*exp(9*x) - 1). - Elmo R. Oliveira, Dec 16 2025

MAPLE

A332194 := n -> 10^(n*2+1)-1-5*10^n;

MATHEMATICA

Array[ 10^(2 # + 1) -1 -5*10^# &, 15, 0]

PROG

(PARI) apply( {A332194(n)=10^(n*2+1)-1-5*10^n}, [0..15])

(Python) def A332194(n): return 10**(n*2+1)-1-5*10^n

CROSSREFS

Cf. (A077782-1)/2 = A183185: 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. A332114 .. A332184 (variants with different repeated digit 1, ..., 8).

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

Sequence in context: A188978 A333502 A202684 * A384848 A364276 A006030

Adjacent sequences: A332191 A332192 A332193 * A332195 A332196 A332197

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Feb 08 2020

STATUS

approved