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A332135 a(n) = (10^(2n+1)-1)/3 + 2*10^n. 1
5, 353, 33533, 3335333, 333353333, 33333533333, 3333335333333, 333333353333333, 33333333533333333, 3333333335333333333, 333333333353333333333, 33333333333533333333333, 3333333333335333333333333, 333333333333353333333333333, 33333333333333533333333333333, 3333333333333335333333333333333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

See A183175 = {1, 2, 17, 79, 118, 162, 177, ...} 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)5(3), updated: June 25, 2017.

Makoto Kamada, Factorization of 33...33533...33, updated Dec 11 2018.

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

FORMULA

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

G.f.: (5 - 202*x - 100*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

A332135 := n -> (10^(2*n+1)-1)/3+2*10^n;

MATHEMATICA

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

PROG

(PARI) apply( {A332135(n)=10^(n*2+1)\3+2*10^n}, [0..15])

(Python) def A332135(n): return 10**(n*2+1)//3+2*10**n

CROSSREFS

Cf. (A077784-1)/2 = A183175: 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. A332125 .. A332195 (variants with different repeated digit 2, ..., 9).

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

Sequence in context: A158105 A203527 A235725 * A225578 A172014 A172855

Adjacent sequences:  A332131 A332132 A332134 * A332136 A332137 A332138

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Feb 09 2020

STATUS

approved

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Last modified July 8 07:34 EDT 2020. Contains 335513 sequences. (Running on oeis4.)