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Search: id:A087606
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| A087606 |
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Smallest k such that n times concatenation of k with itself followed by a 9 is a prime, or 0 if no such number exists. |
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+0
8
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| 1, 2, 0, 1, 1, 0, 1, 11, 0, 64, 5, 0, 2, 31, 0, 1, 5, 0, 10, 65, 0, 41, 212, 0, 5, 79, 0, 41, 160, 0, 5, 94, 0, 8, 82, 0, 23, 43, 0, 40, 26, 0, 391, 119, 0, 212, 4, 0, 1, 160, 0, 134, 28, 0, 208, 50, 0, 248, 35, 0, 113, 43, 0, 79, 7, 0, 70, 170, 0, 64, 94, 0, 19, 86, 0, 10, 118, 0, 34, 98
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: a(3n) = 0. No other term is zero.
a(3n)=0: consider the sum of the digits modulo 3. For the same reason, if a(m) is divisible by 3 then a(m)=0. - Sam Alexander (amnalexander(AT)yahoo.com), Nov 15 2003
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LINKS
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XIAO Gang, Factoris - a program that factorizes huge integers, 1997-1999
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EXAMPLE
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a(2) = 2 as 229 is a prime. but 119 is not.
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MATHEMATICA
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s[b_]:=(v={}; l=Length[b]; Do[v=Join[v, IntegerDigits[b[[k]]]], {k, l}]; v); a[n_]:=If[Mod[n, 3]!= 0, (For[m = 1, ! PrimeQ[10*FromDigits[s[Table[m, {n}]]] +9], m++ ]; m), 0]; Table[a[n], {n, 90}] (Firoozbakht)
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CROSSREFS
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Cf. A086920, A087604, A087605, A087607, A087608, A087609, A087610.
Sequence in context: A060277 A101672 A083731 this_sequence A116799 A057556 A112761
Adjacent sequences: A087603 A087604 A087605 this_sequence A087607 A087608 A087609
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Sep 18 2003
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EXTENSIONS
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More terms from Sam Alexander (amnalexander(AT)yahoo.com), Nov 15 2003
More terms from Farideh Firoozbakht (f.firoozbakht(AT)math.ui.ac.ir), Feb 04 2005
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