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A332192
a(n) = 10^(2n+1) - 1 - 7*10^n.
7
2, 929, 99299, 9992999, 999929999, 99999299999, 9999992999999, 999999929999999, 99999999299999999, 9999999992999999999, 999999999929999999999, 99999999999299999999999, 9999999999992999999999999, 999999999999929999999999999, 99999999999999299999999999999, 9999999999999992999999999999999
OFFSET
0,1
COMMENTS
See A115073 = {1, 8, 9, 352, 530, 697, ...} for the indices of primes.
LINKS
Patrick De Geest, Palindromic Wing Primes: (9)2(9), updated: June 25, 2017.
Makoto Kamada, Factorization of 99...99299...99, updated Dec 11 2018.
FORMULA
a(n) = 9*A138148(n) + 2*10^n = A002283(2n+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.
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 *)
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 A337309
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 08 2020
STATUS
approved