A077706 -id:A077706 - cp's OEIS frontend

A077707 a(n) = A077706(n+1)/A077706(n).

11, 23, 97, 391, 188, 2366, 2269, 2042, 2036, 372, 4742, 3438, 43871, 6642, 47957, 158388, 31666, 15736, 134046, 60877, 90061, 69122, 249766, 123726, 269358, 162881, 1426093, 32082, 1208059, 668822, 541654, 143087, 1399261, 1202267

Offset: 1

Amarnath Murthy, Nov 18 2002

Cf. A077706.

More terms from Ray Chandler, Jul 27 2003

A332116 a(n) = (10^(2n+1)-1)/9 + 5*10^n.

Original entry on oeis.org

6, 161, 11611, 1116111, 111161111, 11111611111, 1111116111111, 111111161111111, 11111111611111111, 1111111116111111111, 111111111161111111111, 11111111111611111111111, 1111111111116111111111111, 111111111111161111111111111, 11111111111111611111111111111, 1111111111111116111111111111111

Offset: 0

M. F. Hasler, Feb 09 2020

See A107126 = {10, 14, 40, 59, 160, 412, ...} for the indices of primes.

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.
Index entries for linear recurrences with constant coefficients, signature (111,-1110,1000).

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).

A332116 := n -> (10^(2*n+1)-1)/9+5*10^n;

Array[(10^(2 # + 1)-1)/9 + 5*10^# &, 15, 0]

apply( {A332116(n)=10^(n*2+1)\9+5*10^n}, [0..15])

def A332116(n): return 10**(n*2+1)//9+5*10**n

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

cp's OEIS Frontend

A077707 a(n) = A077706(n+1)/A077706(n).

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A332116 a(n) = (10^(2n+1)-1)/9 + 5*10^n.

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