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Search: id:A139186
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| A139186 |
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Smallest a(n) = k such that k!/n +- 1 is a twin prime pair. |
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+0
3
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| 3, 4, 6, 4, 11, 4, 10, 5, 6, 8, 21, 5, 7, 6, 22, 10, 7, 5, 8, 10, 16, 6, 13, 43, 9, 26, 17, 11, 6, 27, 20, 59, 7, 12, 24, 32, 91, 13, 67, 7, 48, 11, 15, 15, 32, 8, 45, 14, 9, 6, 10, 22, 9, 9, 37, 22, 14, 58, 9, 11, 7, 41, 6, 33, 98, 22, 47, 20, 8, 13, 8
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Smallest factorial indices k such that ( k!/n-1 , k!/n+1 ) = ( A001359(j) , A006512(j) )
for some twin prime index j.
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FORMULA
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A000142(a(n))/n-1 = A139187(n). A000142(a(n))/n+1 = A139188(n).
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EXAMPLE
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For n=6, solutions to k!/n - 1 = A001359(j) are given by k = 4, 11, 13, 17,..
The smallest k out of these, k=4, is chosen as a(n=6).
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MATHEMATICA
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a = {}; Do[k = 1; While[ ! (PrimeQ[(k! - n)/n] && PrimeQ[(k! + n)/n]), k++ ]; AppendTo[a, k]; Print[a], {n, 1, 6}]; a (*Artur Jasinski*)
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CROSSREFS
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Cf. A139187, A139188.
Sequence in context: A136248 A101432 A023823 this_sequence A047840 A037189 A083342
Adjacent sequences: A139183 A139184 A139185 this_sequence A139187 A139188 A139189
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KEYWORD
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nonn
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AUTHOR
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Artur Jasinski (grafix(AT)csl.pl), Apr 11 2008
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EXTENSIONS
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Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 22 2009
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