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A332113
a(n) = (10^(2n+1)-1)/9 + 2*10^n.
11
3, 131, 11311, 1113111, 111131111, 11111311111, 1111113111111, 111111131111111, 11111111311111111, 1111111113111111111, 111111111131111111111, 11111111111311111111111, 1111111111113111111111111, 111111111111131111111111111, 11111111111111311111111111111, 1111111111111113111111111111111
OFFSET
0,1
COMMENTS
See A107123 = {0, 1, 2, 19, 97, 9818, ...} for the indices of primes.
LINKS
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
Patrick De Geest, Palindromic Wing Primes: (1)3(1), updated: June 25, 2017.
Makoto Kamada, Factorization of 11...11311...11, updated Dec 11 2018.
FORMULA
a(n) = A138148(n) + 3*10^n = A002275(2n+1) + 2*10^n.
G.f.: (3 - 202*x + 100*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
A332113 := n -> (10^(2*n+1)-1)/9+2*10^n;
MATHEMATICA
Array[(10^(2 # + 1)-1)/9 + 2*10^# &, 15, 0]
PROG
(PARI) apply( {A332113(n)=10^(n*2+1)\9+2*10^n}, [0..15])
(Python) def A332113(n): return 10**(n*2+1)//9+2*10**n
CROSSREFS
Cf. (A077779-1)/2 = A107123: indices of primes; A331864 & A331865 (non-palindromic variants).
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332123 .. A332193 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
Sequence in context: A347985 A082439 A082622 * A075597 A262639 A082563
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved