A332118 a(n) = (10^(2n+1) - 1)/9 + 7*10^n.

8, 181, 11811, 1118111, 111181111, 11111811111, 1111118111111, 111111181111111, 11111111811111111, 1111111118111111111, 111111111181111111111, 11111111111811111111111, 1111111111118111111111111, 111111111111181111111111111, 11111111111111811111111111111, 1111111111111118111111111111111

Offset

0,1

Comments

See A107648 = {1, 4, 6, 7, 384, 666, ...} for the indices of primes.

Links

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

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

Patrick De Geest, Palindromic Wing Primes: (1)8(1), updated: June 25, 2017.

Makoto Kamada, Factorization of 11...11811...11, updated Dec 11 2018.

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

Formula

a(n) = A138148(n) + 8*10^n = A002275(2n+1) + 7*10^n.

G.f.: (8 - 707*x + 600*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

A332118 := n -> (10^(2*n+1)-1)/9+7*10^n;

Mathematica

Array[(10^(2 # + 1)-1)/9 + 7*10^# &, 15, 0]

Prog

(PARI) apply( {A332118(n)=10^(n*2+1)\9+7*10^n}, [0..15])
(Python) def A332118(n): return 10**(n*2+1)//9+7*10**n

Crossrefs

Cf. (A077791-1)/2 = A107648: indices of primes.

Cf. A002275 (repunits R_n = (10^n-1)/9), A011557 (10^n).

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes), A077798 (palindromic wing primes), A088281 (primes 1..1x1..1), A068160 (smallest of given length), A053701 (vertically symmetric numbers).

Cf. A332128 .. A332178, A181965 (variants with different repeated digit 2, ..., 9).

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

Sequence in context: A360340 A060593 A130775 * A261825 A203359 A294355

Adjacent sequences: A332115 A332116 A332117 * A332119 A332120 A332121

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved