A051779 Primes of form pq + 2 where p and q are twin primes.

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

Offset: 1

Author

Joe DeMaio (jdemaio(AT)kennesaw.edu), Dec 09 1999

Keywords

• easy
• nonn

Comments

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). - Zak Seidov, Dec 07 2008

Primes of the form (p^2 + q^2)/2, where p and q are twin primes. - Thomas Ordowski and Altug Alkan, Mar 19 2017

Examples

			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.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A048880, A051779, A000040, A001359, A005384, A006512, A037074, A054735.

Cf. A125251. - Zak Seidov, Dec 07 2008

Programs

Maple

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;

Mathematica

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 (* Vladimir Joseph Stephan Orlovsky, Aug 08 2008 *)
Select[(First[#]Last[#]+2)&/@Select[Partition[Prime[Range[2700]], 2,1], Last[#]-First[#]==2&],PrimeQ]  (* Harvey P. Dale, Mar 11 2011 *)
Select[2 + Times @@@ Select[ Partition[ Prime@ Range@ 1350, 2, 1], First[#] + 2 == Last[#] &], PrimeQ] (* Robert G. Wilson v, Mar 12 2001 *)

Formula

{A037074(k) + 2} INTERSECT {A000040}. {A001359(k) * A006512(k) + 2} INTERSECT {A000040}. {A054735(k)^2 + 2*A054735(k) + 2} INTERSECT {A000040}. - Jonathan Vos Post, May 11 2006

Extensions

Edited by R. J. Mathar, Aug 08 2008