Search: id:A007908
Results 1-1 of 1 results found.

%I A007908
%S A007908 1,12,123,1234,12345,123456,1234567,12345678,123456789,12345678910,
%T A007908 1234567891011,123456789101112,12345678910111213,1234567891011121314,
%U A007908 123456789101112131415,12345678910111213141516,1234567891011121314151617
%N A007908 Concatenation of the numbers from 1 to n.
%C A007908 Sometimes called Smarandache consecutive numbers.
%C A007908 Also called the triangle of the gods (see Pickover link).
%C A007908 As n -> infinity, lim((A007908(n))/(prod(i=1,n, 10^floor(1+(log(i)/(log(10))))))) 
               yields the Champernowne constant. - Alexander R. Povolotsky (pevnev(AT)juno.com), 
               May 29 2008, Paolo Lava, Jun 06 2008
%D A007908 Y. Guo and M. Le, Smarandache Concatenated Power Decimals and Their Irrationality, 
               Smarandache Notions Journal, Vol. 9, No. 1-2. 1998, 100-102.
%D A007908 R. K. Guy, Unsolved Problems in Number Theory, A3.
%D A007908 F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 
               1993.
%H A007908 T. D. Noe, <a href="b007908.txt">Table of n, a(n) for n=1..100</a>
%H A007908 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A007908 Clifford Pickover, <a href="http://sprott.physics.wisc.edu/Pickover/trianglegod.htm">
               Triangle of the Gods</a>
%H A007908 R. W. Stephan, <a href="http://me.in-berlin.de/~rws/sm.pdf">Factors and 
               primes in two Smarandache sequences</a>
%H A007908 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>
%H A007908 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               ConsecutiveNumberSequences.html">Link to a section of The World of 
               Mathematics.</a>
%F A007908 a(n)=a(n-1)*10^floor[log10(10*n)]+n - Paolo P. Lava (ppl(AT)spl.at), 
               Feb 01 2008
%F A007908 a(n)=n+a(n-1)*10^A055642(n) - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               May 31 2008
%F A007908 a(n) = prod(a,1,n,10^floor(1+log(10)^(-1)*log(a))) *sum(b,1,n,prod(a,
               1,b,10^floor(log(10)^(-1)*(log(10)+log(a))))^(-1)*b). - Alexander 
               R. Povolotsky and Paolo Lava, Jun 06 2008
%p A007908 A055642 := proc(n) max(1, ilog10(n)+1) ; end: A007908 := proc(n) if n 
               = 1 then 1; else A007908(n-1)*10^A055642(n)+n ; fi ; end: seq(A007908(n),
               n=1..12) ; # R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 
               2008
%p A007908 P:=proc(i) local a,b,n,x; for n from 1 by 1 to i do x:=evalf(product(10^floor(1+log10(a)),
               a=1..n)*sum('product(10^floor(log10(10)+log10(a)),a= 1..b)^(-1)*b',
               'b'=1..n)); od; end: - Alexander R. Povolotsky and Paolo Lava, Jun 
               06 2008
%o A007908 (PARI) A007908(n)= prod(a=1,n,10^floor(1+log(10)^(-1)*log(a)))*sum(b=1,
               n,prod(a=1,b,10^floor(log(10)^(-1)*(log(10)+log(a))))^(-1)*b) - Alexander 
               R. Povolotsky and Paolo Lava, Jun 06 2008
%Y A007908 See A057137 for another version.
%Y A007908 Cf. A033307.
%Y A007908 A053064. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 10 2008]
%Y A007908 Sequence in context: A014824 A060555 A138957 this_sequence A057932 A132943 
               A159901
%Y A007908 Adjacent sequences: A007905 A007906 A007907 this_sequence A007909 A007910 
               A007911
%K A007908 nonn,base
%O A007908 1,2
%A A007908 R. Muller

Search completed in 0.002 seconds