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Search: id:A138479
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| A138479 |
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a(n) = smallest prime p such that 2n + p^2 is another prime, or 0 if no such prime exists. |
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+0
11
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| 3, 3, 5, 3, 3, 5, 3, 5, 5, 3, 3, 7, 0, 3, 7, 3, 3, 5, 3, 7, 5, 3, 5, 5, 3, 3, 5, 0, 3, 7, 3, 3, 29, 0, 3, 5, 3, 5, 5, 3, 5, 5, 0, 3, 7, 3, 3, 19, 3, 3, 5, 3, 5, 7, 0, 5, 5, 0, 3, 11, 3, 5, 5, 3, 3, 5, 0, 11, 5, 3, 3, 7, 0, 3, 7, 0, 3, 5, 3, 11, 7, 3, 5, 5, 3, 3, 5, 0, 7, 7, 3, 3, 5, 3, 3, 7, 0, 11, 5, 0
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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For numbers n such that a(n) = 0 see A138685..
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LINKS
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Eric Weisstein's World of Mathematics, Near-Square Prime
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EXAMPLE
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11=2+3^2 hence a(1)=3
13=4+3^2 hence a(2)=3
31=6+5^2 hence a(3)=5
17=8+3^2 hence a(4)=3
19=10+3^2 hence a(5)=3
37=12+5^2 hence a(6)=5
23=14+3^2 hence a(7)=3
41=16+5^2 hence a(8)=5
43=18+5^2 henec a(9)=5
29=20+3^2 hence a(10)=3
31=22+3^2 hence a(11)=3
73=24+7^2 hence a(12)=7
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MATHEMATICA
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a = {}; Do[ p = 0; While[ (! PrimeQ[ 2*n + Prime[ p + 1 ]2 ]) && (p < 1000), p++ ]; If[ p < 1000, AppendTo[ a, Prime[ p + 1 ] ], AppendTo[ a, 0 ] ], {n, 1, 150} ]; a (*Artur Jasinski, Mar 26 2008*)
a[n_]:=If[Mod[n, 3]!=1, (For[m=1, !PrimeQ[2n+Prime[m]^2], m++ ]; Prime[m]), If[ !PrimeQ[2n+9], 0, 3]]; Table[a[n], {n, 100}] - Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 28 2008
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CROSSREFS
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Cf. A002373, A020481, A049613, A059324 (?).
Sequence in context: A013606 A054906 A020483 this_sequence A136019 A063714 A113965
Adjacent sequences: A138476 A138477 A138478 this_sequence A138480 A138481 A138482
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KEYWORD
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nonn,hard
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AUTHOR
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Philippe LALLOUET (philip.lallouet(AT)orange.fr), Mar 20 2008
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EXTENSIONS
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More terms from Artur Jasinski (grafix(AT)csl.pl) and Farideh Firoozbakht (mymontain(AT)yahoo.com), Mar 26 2008
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