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A332114
a(n) = (10^(2n+1)-1)/9 + 3*10^n.
6
4, 141, 11411, 1114111, 111141111, 11111411111, 1111114111111, 111111141111111, 11111111411111111, 1111111114111111111, 111111111141111111111, 11111111111411111111111, 1111111111114111111111111, 111111111111141111111111111, 11111111111111411111111111111, 1111111111111114111111111111111
OFFSET
0,1
COMMENTS
See A107124 = {2, 3, 32, 45, 1544, ...} 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)4(1), updated: June 25, 2017.
Makoto Kamada, Factorization of 11...11411...11, updated Dec 11 2018.
FORMULA
a(n) = A138148(n) + 4*10^n = A002275(2n+1) + 3*10^n.
G.f.: (4 - 303*x + 200*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
A332114 := n -> (10^(2*n+1)-1)/9+3*10^n;
MATHEMATICA
Array[(10^(2 # + 1)-1)/9 + 3*10^# &, 15, 0]
PROG
(PARI) apply( {A332114(n)=10^(n*2+1)\9+3*10^n}, [0..15])
(Python) def A332114(n): return 10**(n*2+1)//9+3*10**n
CROSSREFS
Cf. (A077780-1)/2 = A107124: indices of primes; A331866 & A331867 (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. A332124 .. A332194 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
Sequence in context: A215606 A119038 A048432 * A262653 A299061 A299722
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved