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Search: id:A146569
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| A146569 |
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Numbers m with the property that shifting the rightmost digit of m to the left end multiplies the number by 4. |
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+0
2
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| 102564, 128205, 153846, 179487, 205128, 230769, 102564102564, 128205128205, 153846153846, 179487179487, 205128205128, 230769230769, 102564102564102564, 128205128205128205, 153846153846153846, 179487179487179487
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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a(13) <= 102564102564102564. [From Donovan Johnson (donovan.johnson(AT)yahoo.com), Jun 06 2009]
The condition is equivalent to the numbers being of the form 10*m+d with a k-digit number m and a non-zero digit d such that 4*(10*m+d) = 10^k * d + m, i.e. 39*m = (10^k - 4)*d. Checking modulo 13, this implies k = 5 (mod 6). Also, m >= 10^(k-1) implies d >= 4. Each such k and d leads to a solution. [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 26 2009]
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FORMULA
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If n = 6*k + r with 1 <= r <=6, then a(n) = (10^(6*k)-1)/(10^6-1) * a(r) as well as a(n) = floor( (r+3)/39 * 10^(6*(k+1)) ) [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 26 2009]
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PROGRAM
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(PARI) a(n) = local(r=(n-1)%6+1, k=(n-r)/6); floor((r+3)/39*10^(6*(k+1))) [From Hagen von Eitzen (math(AT)von-eitzen.de), Jun 26 2009]
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CROSSREFS
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Cf. A146088.
Sequence in context: A074669 A010329 A034089 this_sequence A081463 A014884 A015330
Adjacent sequences: A146566 A146567 A146568 this_sequence A146570 A146571 A146572
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KEYWORD
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nonn,base
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AUTHOR
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N. J. A. Sloane, based on correspondence from William A. Hoffman III (whoff(AT)robill.com), Apr 10 2009
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EXTENSIONS
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a(7)-a(12) from Donovan Johnson (donovan.johnson(AT)yahoo.com), Jun 06 2009
More terms from Hagen von Eitzen (math(AT)von-eitzen.de), Jun 26 2009
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