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Search: id:A031973
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| 1, 2, 7, 40, 341, 3906, 55987, 960800, 19173961, 435848050, 11111111111, 313842837672, 9726655034461, 328114698808274, 11966776581370171, 469172025408063616, 19676527011956855057, 878942778254232811938
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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These are the generalized repunits of length n+1 in base n for all n >= 1: a(n) expressed in base n is 111...111 (n+1 1's): a(1) = 1^0 + 1^1 = 2 = A000042(2), a(2) = 2^0 + 2^1 + 2^2 = 7 = A000225(3), a(3) = 3^0 + 3^1 + 3^2 + 3^3 = 40 = A003462(4), etc., a(10) = 10^0 + 10^1 + 10^2 + ... + 10^9 + 10^10 = 11111111111 = A002275(11), etc. - Rick L. Shepherd (rshepherd2(AT)hotmail.com), Aug 26 2004
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FORMULA
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a(n) = (n^(n+1)-1)/(n-1) = (A007778(n)-1)/(n-1) = A023037(n)+A000312(n) = A031972(n)+1. - Henry Bottomley (se16(AT)btinternet.com), Apr 04 2003
a(n) = A125118(n,n-2) for n>2. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.com), Nov 21 2006
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EXAMPLE
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a(3) = 3^0 + 3^1 + 3^2 + 3^3 = 40.
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CROSSREFS
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Cf. A000042 (unary representations), A000225 (2^n-1: binary repunits shown in decimal), A003462 ((3^n-1)/2: ternary repunits shown in decimal), A002275 ((10^n-1)/9: decimal repunits).
Sequence in context: A105625 A135082 A102317 this_sequence A132785 A064626 A137731
Adjacent sequences: A031970 A031971 A031972 this_sequence A031974 A031975 A031976
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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