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Search: id:A067895
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| A067895 |
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Write 2^n, 2^n+1, 2^n+2, ..., 2^(n+1)-1 in binary and add as if they were decimal numbers. |
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+0
3
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| 1, 21, 422, 8444, 168888, 3377776, 67555552, 1351111104, 27022222208, 540444444416, 10808888888832, 216177777777664, 4323555555555328, 86471111111110656, 1729422222222221312, 34588444444444442624, 691768888888888885248, 13835377777777777770496, 276707555555555555540992
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: (1-x)/(1-22x+40x^2). a(n)=2^(n-1)*(19*10^n-1)/9=22a(n-1)-40a(n-2).
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EXAMPLE
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2^2 to 2^3-1 = 4 through 7 = 100, 101, 110 and 111 in binary and when summed = 422.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, 2^(n-1)*(19*10^n-1)/9)
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CROSSREFS
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Cf. A067894.
Sequence in context: A083043 A097833 A064108 this_sequence A092499 A009965 A041842
Adjacent sequences: A067892 A067893 A067894 this_sequence A067896 A067897 A067898
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KEYWORD
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nonn,base,easy
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AUTHOR
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njas, May 15 2003
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