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A261544
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a(n) = Sum_{k=0..n} 1000^k.
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4
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1, 1001, 1001001, 1001001001, 1001001001001, 1001001001001001, 1001001001001001001, 1001001001001001001001, 1001001001001001001001001, 1001001001001001001001001001, 1001001001001001001001001001001, 1001001001001001001001001001001001
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OFFSET
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0,2
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COMMENTS
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A sequence of palindromic numbers.
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LINKS
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FORMULA
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a(n) = (1000^(n + 1) - 1)/999.
a(n) = 1001*a(n-1) - 1000*a(n-2). - Colin Barker, Aug 24 2015
E.g.f.: (1/999)*(1000000*exp(1000*x) - exp(x)). - G. C. Greubel, Aug 29 2015
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EXAMPLE
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a(n) is the binary representation of A023001
-------------------------------------------------
1 ........................................... 1
1001 ........................................ 9
1001001 ..................................... 73
1001001001 ................................ 585
1001001001001 ............................ 4681
1001001001001001 ........................ 37449
1001001001001001001 .................... 299593
1001001001001001001001 ................ 2396745
1001001001001001001001001 ............ 19173961, etc.
(End)
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MATHEMATICA
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Table[(1000^(n + 1) - 1)/999, {n, 0, 15}]
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PROG
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(PARI) Vec(1 / ((x-1)*(1000*x-1)) + O(x^20)) \\ Colin Barker, Aug 24 2015
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CROSSREFS
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Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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