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A062397
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a(n) = 10^n + 1.
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34
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2, 11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001, 1000000001, 10000000001, 100000000001, 1000000000001, 10000000000001, 100000000000001, 1000000000000001, 10000000000000001, 100000000000000001
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OFFSET
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0,1
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COMMENTS
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The first three terms (indices 0, 1 and 2) are the only known primes. Moreover, the terms not of the form a(2^k) are all composite, except for a(0). 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 [Edited based on the comment by Jeppe Stig Nielsen, Oct 17 2019]
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).
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FORMULA
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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)
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MATHEMATICA
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LinearRecurrence[{11, -10}, {2, 11}, 18] (* Ray Chandler, Aug 26 2015 *)
10^Range[0, 20]+1 (* Harvey P. Dale, Jan 21 2020 *)
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PROG
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(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
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CROSSREFS
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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), A185121.
Sequence in context: A036953 A254320 A115062 * A158578 A003617 A114018
Adjacent sequences: A062394 A062395 A062396 * A062398 A062399 A062400
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KEYWORD
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easy,nonn
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AUTHOR
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Henry Bottomley, Jun 22 2001
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STATUS
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approved
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