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A062397 a(n) = 10^n + 1. 33
2, 11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 100000000001, 1000000000001, 10000000000001, 100000000000001, 1000000000000001, 10000000000000001, 100000000000000001 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Warning, this comment appears to be false. - N. J. A. Sloane, Oct 17 2019. The first three terms (indices 0, 1 and 2) are the only primes. Indeed, for all n >= 0, a(2n+1) is divisible by 11, a(4n+2) is divisible by 101, a(8n+4) is divisible by 73, a(16n+8) is divisible by 17, a(32n+16) is divisible by 353, a(64n+32) is divisible by 19841, etc. - M. F. Hasler, Nov 03 2018

That comment cannot work when the exponent is a power of two. As an example, it gives no divisor for a(16384) (none is known). It is currently unknown if a(2^31) is prime. - Jeppe Stig Nielsen, Oct 17 2019

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (11,-10).

FORMULA

a(n) = 10*a(n-1) - 9 = A011557(n) + 1 = A002283(n) + 2.

From Mohammad K. Azarian, Jan 02 2009: (Start)

G.f.: 1/(1-x) + 1/(1-10*x).

E.g.f.: exp(x) + exp(10*x). (End)

MATHEMATICA

LinearRecurrence[{11, -10}, {2, 11}, 18] (* Ray Chandler, Aug 26 2015 *)

PROG

(MAGMA) [10^n + 1: n in [0..35]]; // Vincenzo Librandi, Apr 30 2011

(PARI) a(n)=10^n+1 \\ Charles R Greathouse IV, Sep 24 2015

CROSSREFS

Except for the initial term, essentially the same as A000533. Cf. A054977, A007395, A000051, A034472, A052539, A034474, A062394, A034491, A062395, A062396, A007689, A063376, A063481, A074600-A074624, A034524, A178248, A228081 for numbers one more than powers, i.e., this sequence translated from base n (> 2) to base 10.

Cf. A002283, A011557.

Cf. A038371 (smallest prime factor).

Sequence in context: A036953 A254320 A115062 * A158578 A003617 A114018

Adjacent sequences:  A062394 A062395 A062396 * A062398 A062399 A062400

KEYWORD

easy,nonn,changed

AUTHOR

Henry Bottomley, Jun 22 2001

STATUS

approved

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Last modified October 17 21:57 EDT 2019. Contains 328134 sequences. (Running on oeis4.)