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A052379
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Number of integers from 1 to 10^(n+1)-1 that lack 0 and 1 as a digit.
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9
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8, 72, 584, 4680, 37448, 299592, 2396744, 19173960, 153391688, 1227133512, 9817068104, 78536544840, 628292358728, 5026338869832, 40210710958664, 321685687669320, 2573485501354568, 20587884010836552, 164703072086692424
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..400
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FORMULA
| a(n) = (8^(n+2) - 1)/7 -1
G.f.: 8/((1-x)*(1-8*x)). - R. J. Mathar, Nov 19 2007
a(n) = 8*a(n-1) + 8.
a(n) = sum(k=1,n, 8^n ).
Conjecture: a(n)=A023001(n+2)-1 . - R. J. Mathar, May 18 2007. Comment from Vim Wenders (vim(AT)gmx.li), Mar 26 2008: The conjecture is true: the g.f. leads to the closed form a(n) = -8/7*(1^n) + 64/7*(8^n) = (-8 + 64*8^n)/7 = (-8 + 8^(n+2))/7 = (8^(n+2) - 1)/7 -1 = A023001(n+2)-1.
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EXAMPLE
| For n=1, the numbers from 1 to 99 which *have* 0 or 1 as a digit are the numbers 1 and 10, 20, 30, ..., 90 and 11, 12, ..., 18, 19 and 21, 31, ..., 91. So a(1) = 99 - 27 = 72.
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PROG
| (MAGMA) [(8^(n+2) - 1)/7 -1: n in [0..20]]; // Vincenzo Librandi, Jul 04 2011
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CROSSREFS
| Cf. A024101, A052386.
Sequence in context: A082141 A054615 A111919 * A158798 A062541 A057091
Adjacent sequences: A052376 A052377 A052378 * A052380 A052381 A052382
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KEYWORD
| easy,nonn,base
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AUTHOR
| Odimar Fabeny (fabeny(AT)braznet.com.br), Mar 12 2000
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EXTENSIONS
| More terms and revised description from James A. Sellers (sellersj(AT)math.psu.edu), Mar 13 2000
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