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Search: id:A007088
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| A007088 |
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Numbers written in base 2.
(Formerly M4679)
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+0
325
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| 0, 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111, 10000, 10001, 10010, 10011, 10100, 10101, 10110, 10111, 11000, 11001, 11010, 11011, 11100, 11101, 11110, 11111, 100000, 100001, 100010, 100011, 100100, 100101, 100110, 100111
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Or, numbers that are sums of distinct powers of 10.
Or, decimal numbers that only mention 0 and 1.
Complement of A136399; A064770(a(n)) = a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 30 2007
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LINKS
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Franklin T. Adams-Watters, Table of n, a(n) for n = 0..8192
Index entries for sequences related to binary expansion of n
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FORMULA
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a(n)=Sum{d(i)*10^i: i=0, 1, ..., m}, where Sum{d(i)*2^i: i=0, 1, ..., m} is the base 2 representation of n.
a(n)=(1/2)*sum(i => 0, (1-(-1)^floor(n/2^i))*10^i). - Benoit Cloitre (benoit7848c(AT)orange.fr), Nov 20 2001
a(n) = A097256(n)/9.
a(2n) = 10*a(n), a(2n+1) = a(2n)+1.
G.f. 1/(1-x) * Sum_{k>=0} 10^k * x^{2^k}/(1+x^{2^k}) - for sequence as decimal integers. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 16 2006
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EXAMPLE
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a(6)=110 because (1/2)*((1-(-1)^6)*10^0+(1-(-1)^3)*10^1+(1-(-1)^1)*10^2) = 10+100
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MATHEMATICA
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Table[ FromDigits[ IntegerDigits[n, 2]], {n, 0, 39}]
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PROGRAM
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(PARI) a(n)=subst(Pol(binary(n)), x, 10)
(PARI) a(n)=if(n<=0, 0, n%2+10*a(n\2))
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CROSSREFS
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The basic sequences concerning the binary expansion of n are this one, A000788, A000069, A001969, A023416, A059015, A000120.
Cf. A000042, A007089, A007090, A007091, A007092, A007093, A007094 & A007095.
Cf. A000695, A005836, A033042-A033052.
Sequence in context: A045953 A136830 A081551 this_sequence A115848 A136814 A136809
Adjacent sequences: A007085 A007086 A007087 this_sequence A007089 A007090 A007091
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KEYWORD
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nonn,nice,easy
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AUTHOR
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njas, Robert G. Wilson v (rgwv(AT)rgwv.com)
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