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A332138 a(n) = (10^(2*n+1)-1)/3 + 5*10^n. 2
8, 383, 33833, 3338333, 333383333, 33333833333, 3333338333333, 333333383333333, 33333333833333333, 3333333338333333333, 333333333383333333333, 33333333333833333333333, 3333333333338333333333333, 333333333333383333333333333, 33333333333333833333333333333, 3333333333333338333333333333333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A183177 = {1, 7, 85, 94, 273, 356, ...} 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: (3)8(3), updated: June 25, 2017.

Makoto Kamada, Factorization of 33...33833...33, updated Dec 11 2018.

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

FORMULA

a(n) = 3*A138148(n) + 8*10^n = A002277(2n+1) + 5*10^n.

G.f.: (8 - 505*x + 200*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

A332138 := n -> (10^(2*n+1)-1)/3+5*10^n;

MATHEMATICA

Array[ (10^(2 # + 1)-1)/3 + 5*10^# &, 15, 0]

PROG

(PARI) apply( {A332138(n)=10^(n*2+1)\3+5*10^n}, [0..15])

(Python) def A332138(n): return 10**(n*2+1)//3+5*10**n

CROSSREFS

Cf. (A077792-1)/2 = A183177: indices of primes.

Cf. A002275 (repunits R_n = (10^n-1)/9), A002277 (3*R_n), A011557 (10^n).

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

Cf. A332118 .. A332178, A181965 (variants with different repeated digit 1, ..., 9).

Cf. A332130 .. A332139 (variants with different middle digit 0, ..., 9).

Sequence in context: A266920 A072447 A326877 * A225698 A151932 A265865

Adjacent sequences:  A332135 A332136 A332137 * A332139 A332140 A332141

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Feb 09 2020

STATUS

approved

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Last modified September 27 04:33 EDT 2022. Contains 357052 sequences. (Running on oeis4.)