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Search: id:A007924
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| A007924 |
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n written in base where place values are 1 and primes. |
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+0
3
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| 0, 1, 10, 100, 101, 1000, 1001, 10000, 10001, 10010, 10100, 100000, 100001, 1000000, 1000001, 1000010, 1000100, 10000000, 10000001, 100000000, 100000001, 100000010, 100000100, 1000000000, 1000000001, 1000000010, 1000000100, 1000000101
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Any nonnegative number can be written as a sum of distinct primes + e, where e is 0 or 1.
Terms contain only digits 0 and 1.
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REFERENCES
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F. Smarandache, "Only Problems, not Solutions!", Xiquan Publ., Phoenix-Chicago, 1993.
F. Smarandache, Definitions solved and unsolved problems, conjectures and theorems in number theory and geometry, edited by M. Perez, Xiquan Publishing House 2000
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LINKS
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M. L. Perez et al., eds., Smarandache Notions Journal
C. Rivera, Prime puzzle 78
F. Smarandache, Only Problems, Not Solutions!
F. Smarandache, Definitions, Solved and Unsolved Problems, Conjectures, ...
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FORMULA
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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
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EXAMPLE
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4 = 3 + 1, so a(4) = 101.
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CROSSREFS
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Sequence in context: A019513 A037415 A014417 this_sequence A115794 A105424 A115832
Adjacent sequences: A007921 A007922 A007923 this_sequence A007925 A007926 A007927
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KEYWORD
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nonn,easy
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AUTHOR
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R. Muller
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EXTENSIONS
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Additional references from Felice Russo (felice.russo(AT)katamail.com), Sep 14 2001
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