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Search: id:A051779
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| A051779 |
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Primes of form pq+2 where p and q are twin primes. |
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+0
7
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| 17, 37, 22501, 32401, 57601, 72901, 176401, 324901, 1664101, 1742401, 5336101, 6502501, 7452901, 11289601, 11492101, 18147601, 21622501, 34222501, 34574401, 40449601, 45968401, 81000001, 85377601, 92736901, 110880901, 118592101
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Starting with 3rd term, 22501, all terms are of the form 900n^2+1 with n=5, 6, 8, 9, 14, 19, 43, 44, 77, 85 (A125251) [From Zak Seidov (zakseidov(AT)yahoo.com), Dec 07 2008]
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FORMULA
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{A037074(k) + 2} INTERSECT {A000040}. {A001359(k) * A006512(k) + 2} INTERSECT {A000040}. {A054735(k)^2 + 2*A054735(k) + 2} INTERSECT {A000040}. - Jonathan Vos Post (jvospost3(AT)gmail.com), May 11 2006
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EXAMPLE
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The third term 22501 is a member of the sequence because 22501=149*151+2, 22501 is prime and {149,151} is a twin prime pair.
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MAPLE
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with (numtheory): for n from 1 to 2000 do if (ithprime(n+1)-ithprime(n)=2) then if (tau(ithprime(n)*ithprime(n+1)+2)=2) then print(ithprime(n), ithprime(n+1), ithprime(n)*ithprime(n+1)+2); fi; fi; od;
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MATHEMATICA
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lst={}; Do[p=Prime[n]; If[Length[Divisors[p-2]]==4&&(Divisors[p-2][[3]]-Divisors[p-2][[2]])==2, AppendTo[lst, p]], {n, 6*10^5}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Aug 08 2008]
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CROSSREFS
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Cf. A048880, A051779, A000040, A001359, A005384, A006512, A037074, A054735.
A125251 [From Zak Seidov (zakseidov(AT)yahoo.com), Dec 07 2008]
Sequence in context: A093343 A153685 A121710 this_sequence A139579 A125248 A156777
Adjacent sequences: A051776 A051777 A051778 this_sequence A051780 A051781 A051782
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KEYWORD
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easy,nonn
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AUTHOR
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Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 09 1999
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EXTENSIONS
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Edited by R. J. Mathar, Aug 08 2008
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