Search: id:A007924
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%I A007924
%S A007924 0,1,10,100,101,1000,1001,10000,10001,10010,10100,100000,100001,1000000,
%T A007924 1000001,1000010,1000100,10000000,10000001,100000000,100000001,100000010,
%U A007924 100000100,1000000000,1000000001,1000000010,1000000100,1000000101
%N A007924 n written in base where place values are 1 and primes.
%C A007924 Any nonnegative number can be written as a sum of distinct primes + e, 
               where e is 0 or 1.
%C A007924 Terms contain only digits 0 and 1.
%D A007924 F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 
               1993.
%D A007924 F. Smarandache, Definitions solved and unsolved problems, conjectures 
               and theorems in number theory and geometry, edited by M. Perez, Xiquan 
               Publishing House 2000
%H A007924 M. L. Perez et al., eds., <a href="http://www.gallup.unm.edu/~smarandache/
               ">Smarandache Notions Journal</a>
%H A007924 C. Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_141.htm">
               Prime puzzle 78</a>
%H A007924 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/OPNS.pdf">
               Only Problems, Not Solutions!</a>
%H A007924 F. Smarandache, <a href="http://www.gallup.unm.edu/~smarandache/Definitions-book.pdf">
               Definitions, Solved and Unsolved Problems, Conjectures, ... </a>
%F A007924 a(n) is the binary representation of b(n) = 2^pi(n) + b(n-p(pi(n))) for 
               n > 0 and a(0) = b(0)= 0, where pi(k) = number of primes <= k (A000720) 
               and p(k) = k-th prime (A008578). - Frank Ellermann (frank.ellermann(AT)t-online.de), 
               Dec 18, 2001
%e A007924 4 = 3 + 1, so a(4) = 101.
%Y A007924 Sequence in context: A019513 A037415 A014417 this_sequence A115794 A105424 
               A115832
%Y A007924 Adjacent sequences: A007921 A007922 A007923 this_sequence A007925 A007926 
               A007927
%K A007924 nonn,easy
%O A007924 0,3
%A A007924 R. Muller
%E A007924 Additional references from Felice Russo (felice.russo(AT)katamail.com), 
               Sep 14 2001

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