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A332197 a(n) = 10^(2n+1) - 1 - 2*10^n. 16
7, 979, 99799, 9997999, 999979999, 99999799999, 9999997999999, 999999979999999, 99999999799999999, 9999999997999999999, 999999999979999999999, 99999999999799999999999, 9999999999997999999999999, 999999999999979999999999999, 99999999999999799999999999999, 9999999999999997999999999999999 (list; graph; refs; listen; history; text; internal format)
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
Patrick De Geest, Palindromic Wing Primes: (9)7(9), updated June 25, 2017.
Makoto Kamada, Factorization of 99...99799...99, updated Dec 11 2018.
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
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 08 2020
STATUS
approved

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Last modified June 16 19:52 EDT 2024. Contains 373432 sequences. (Running on oeis4.)