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A332116 a(n) = (10^(2n+1)-1)/9 + 5*10^n. 5
6, 161, 11611, 1116111, 111161111, 11111611111, 1111116111111, 111111161111111, 11111111611111111, 1111111116111111111, 111111111161111111111, 11111111111611111111111, 1111111111116111111111111, 111111111111161111111111111, 11111111111111611111111111111, 1111111111111116111111111111111 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
See A107126 = {10, 14, 40, 59, 160, 412, ...} 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)6(1), updated: June 25, 2017.
Makoto Kamada, Factorization of 11...11611...11, updated Dec 11 2018.
FORMULA
a(n) = A138148(n) + 6*10^n = A002275(2n+1) + 5*10^n.
G.f.: (6 - 505*x + 400*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
A332116 := n -> (10^(2*n+1)-1)/9+5*10^n;
MATHEMATICA
Array[(10^(2 # + 1)-1)/9 + 5*10^# &, 15, 0]
PROG
(PARI) apply( {A332116(n)=10^(n*2+1)\9+5*10^n}, [0..15])
(Python) def A332116(n): return 10**(n*2+1)//9+5*10**n
CROSSREFS
Cf. (A077706-1)/2 = A107126: indices of primes.
Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).
Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).
Cf. A332126 .. A332196 (variants with different repeated digit 2, ..., 9).
Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).
Sequence in context: A120277 A241453 A193370 * A015086 A052466 A280477
KEYWORD
nonn,base,easy
AUTHOR
M. F. Hasler, Feb 09 2020
STATUS
approved

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Last modified March 28 08:22 EDT 2024. Contains 371236 sequences. (Running on oeis4.)