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| A059583
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Each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(1),..,c(n) so that the reduced fraction 1 c(1) 2 c(2) 3 c(3) 5 ... c(n) prime(n) is equal to (k*m+1)/m for a positive integer m and a nonnegative integer k.
(history;
published version)
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#45 by N. J. A. Sloane at Sat Oct 01 13:15:39 EDT 2022
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#44 by N. J. A. Sloane at Sat Oct 01 13:15:37 EDT 2022
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| NAME
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Each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(1),..,c(n) so that the value of thereduced fraction 1 c(1) 2 c(2) 3 c(3) 5,.., ... c(n) prime(n-th) is primeequal is " remainder = to (k*m+1 ".)/m for a positive integer m and a nonnegative integer k.
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| COMMENTS
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In the definition, " remainder = 1 " means that the resulting fraction, when reduced to its lowest terms, has the form (k*m+1)/m for a positive integers m and a nonnegative integer k. - N. J. A. Sloane, Sep 30 2022
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| EXTENSIONS
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Definition clarified by N. J. A. Sloane, Oct 01 2022
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| STATUS
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approved
editing
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#43 by N. J. A. Sloane at Sat Oct 01 13:12:30 EDT 2022
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#42 by Rémy Sigrist at Sat Oct 01 07:13:06 EDT 2022
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#41 by Rémy Sigrist at Sat Oct 01 07:12:58 EDT 2022
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| NAME
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Each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(1),..,c(n) so that the value of the fraction fraction11 c(1) 2 c(2) 3 c(3) 5,.., c(n) n-th prime is " remainder = 1 ".
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| STATUS
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proposed
editing
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Discussion
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| Sat Oct 01
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| Rémy Sigrist: typo
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#40 by N. J. A. Sloane at Fri Sep 30 23:04:06 EDT 2022
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Discussion
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| Sat Oct 01
| 06:22
| Rémy Sigrist: "has the form (k*m+1)/m" could be moved into the name
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#39 by N. J. A. Sloane at Fri Sep 30 23:04:03 EDT 2022
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| NAME
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Each c(i) is "multiply" (*) or "divide" (/); a(n) is number of choices for c(1),..,c(n) so that the value of the 1fraction1 c(1) 2 c(2) 3 c(3) 5,.., c(n) n-th prime is " remainder = 1 ".
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#38 by N. J. A. Sloane at Fri Sep 30 23:02:04 EDT 2022
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| COMMENTS
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In the definition, " remainder = 1 " means that the resulting fraction, when reduced to its lowest terms, has the form (k*m+1)/m for a positive integers m and a nonnegative integer k. - N. J. A. Sloane, Sep 30 2022
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#37 by N. J. A. Sloane at Fri Sep 30 22:57:14 EDT 2022
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| EXAMPLE
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a(For n = 4) = 5: there are five possibilities: 1/2/3/5/7 = 1/210, 1/2*3/5*7 = 21/10, 1/2*3*5/7 = 15/14, 1/2*3*5*7 = 105/2, and 1*2/3*5*7 = 70/3. So a(4) = 5.
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| STATUS
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proposed
editing
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#36 by Michael S. Branicky at Fri Sep 30 22:49:50 EDT 2022
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