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Search: id:A105330
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| A105330 |
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Numbers n such that 2^(n+1)+2n+1 is prime. |
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+0
3
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| 0, 1, 2, 3, 4, 7, 10, 13, 14, 26, 40, 49, 50, 110, 142, 170, 315, 349, 502, 842, 1251, 1630, 2054, 2906, 3482, 5110, 5227, 5620, 8224, 8788, 8912, 13027, 16243, 17222, 28557, 46532, 54974, 92866, 93093, 120855, 155416
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OFFSET
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1,3
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COMMENT
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If n is in the sequence & m=2^n*(2^(n+1)+2n+1) then sigma(m)+tau(m) =2m because sigma(m)=(2^(n+1)-1)*(2^(n+1)+2n+2), tau(m)=2*(n+1) so sigma(m)+tau(m)=(2^(n+1)-1)*(2^(n+1)+2n+2)+2*(n+1)=2m. Hence 2^A105330*(2^(A105330+1)+2*A105330+1) is a subsequence of A083874. A105331 is this subsequence. Next term is greater than 30500.
No other n < 10^5. -T. D. Noe (noe(AT)sspectra.com), Jun 23 2008
No other n < 300000. [From T. D. Noe (noe(AT)sspectra.com), Apr 03 2009]
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EXAMPLE
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110 is in the sequence because 2^111+2*110+1=2596148429267413814265248164610269 is prime.
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MATHEMATICA
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Do[If[PrimeQ[2^(m + 1) + 2m + 1], Print[m]], {m, 0, 30500}]
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CROSSREFS
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Cf. A083874, A105331.
Sequence in context: A117220 A118426 A082008 this_sequence A097545 A073627 A062042
Adjacent sequences: A105327 A105328 A105329 this_sequence A105331 A105332 A105333
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KEYWORD
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more,nonn
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AUTHOR
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Farideh Firoozbakht (mymontain(AT)yahoo.com), Apr 28 2005
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EXTENSIONS
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4 more terms from T. D. Noe (noe(AT)sspectra.com), Jun 23 2008
Added two more terms -- T. D. Noe (noe(AT)sspectra.com), Apr 03 2009
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