login
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
OFFSET
0,1
COMMENTS
See A107126 = {10, 14, 40, 59, 160, 412, ...} for the indices of primes.
LINKS
Patrick De Geest, Palindromic Wing Primes: (1)6(1), updated: June 25, 2017.
Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).
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.
E.g.f.: exp(x)*(10*exp(99*x) + 45*exp(9*x) - 1)/9. - Stefano Spezia, Jul 13 2024
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