A332117 a(n) = (10^(2*n+1) - 1)/9 + 6*10^n.

7, 171, 11711, 1117111, 111171111, 11111711111, 1111117111111, 111111171111111, 11111111711111111, 1111111117111111111, 111111111171111111111, 11111111111711111111111, 1111111111117111111111111, 111111111111171111111111111, 11111111111111711111111111111, 1111111111111117111111111111111

Offset

0,1

Comments

See A107127 = {0, 3, 33, 311, 2933, ...} for the indices of primes.

Links

Table of n, a(n) for n=0..15.

Patrick De Geest, Palindromic Wing Primes: (1)7(1), updated: June 25, 2017.

Brady Haran and Simon Pampena, Glitch Primes and Cyclops Numbers, Numberphile video (2015).

Makoto Kamada, Factorization of 11...11711...11, updated Dec 11 2018.

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

Formula

a(n) = A138148(n) + 7*10^n = A002275(2*n+1) + 6*10^n.

G.f.: (7 - 606*x + 500*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) + 54*exp(9*x) - 1)/9. - Elmo R. Oliveira, Dec 16 2025

Maple

A332117 := n -> (10^(2*n+1)-1)/9+6*10^n;

Mathematica

Array[(10^(2 # + 1)-1)/9 + 6*10^# &, 15, 0]

Prog

(PARI) apply( {A332117(n)=10^(n*2+1)\9+6*10^n}, [0..15])
(Python) def A332117(n): return 10**(n*2+1)//9+6*10**n

Crossrefs

Cf. (A077789-1)/2 = A107127: 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. A332127 .. A332197 (variants with different repeated digit 2, ..., 9).

Cf. A332112 .. A332119 (variants with different middle digit 2, ..., 9).

Sequence in context: A178019 A337676 A266306 * A226598 A075599 A012500

Adjacent sequences: A332114 A332115 A332116 * A332118 A332119 A332120

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved