A332115 a(n) = (10^(2n+1)-1)/9 + 4*10^n.

5, 151, 11511, 1115111, 111151111, 11111511111, 1111115111111, 111111151111111, 11111111511111111, 1111111115111111111, 111111111151111111111, 11111111111511111111111, 1111111111115111111111111, 111111111111151111111111111, 11111111111111511111111111111, 1111111111111115111111111111111

Offset

0,1

Comments

See A107125 = {0, 1, 7, 45, 115, 681, 1248, ...} 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)5(1), updated: June 25, 2017.

Makoto Kamada, Factorization of 11...11511...11, updated Dec 11 2018.

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

Formula

a(n) = A138148(n) + 5*10^n = A002275(2n+1) + 4*10^n.

G.f.: (5 - 404*x + 300*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

A332115 := n -> (10^(2*n+1)-1)/9+4*10^n;

Mathematica

Array[(10^(2 # + 1)-1)/9 + 4*10^# &, 15, 0]

Prog

(PARI) apply( {A332115(n)=10^(n*2+1)\9+4*10^n}, [0..15])
(Python) def A332115(n): return 10**(n*2+1)//9+4*10**n

Crossrefs

Cf. (A077783-1)/2 = A107125: indices of primes; A331868 & A331869 (non-palindromic variants).

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

Cf. A138148 (cyclops numbers with binary digits), A002113 (palindromes).

Cf. A332125 .. A332195 (variants with different repeated digit 2, ..., 9).

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

Sequence in context: A181979 A258486 A082623 * A262655 A075598 A214691

Adjacent sequences: A332112 A332113 A332114 * A332116 A332117 A332118

Keyword

nonn,base,easy

Author

M. F. Hasler, Feb 09 2020

Status

approved