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A118072 Primes which are the sum of a twin prime pair - 1. 3
7, 11, 23, 59, 83, 359, 383, 479, 563, 839, 863, 1283, 1319, 1619, 2039, 2063, 2099, 2459, 2579, 2903, 2963, 3863, 4259, 4283, 4679, 5099, 5939, 6599, 6659, 6719, 6779, 7079 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subsequence of A072669. - Paolo P. Lava, Dec 21 2007

Dickson's conjecture implies this sequence is infinite. - Charles R Greathouse IV, Apr 18 2013

LINKS

Table of n, a(n) for n=1..32.

FORMULA

{A001359(k) + A006512(k) - 1} INTERSECT {A000040}. {A054735(k) - 1} INTERSECT {A000040}. {2*A001359(k) + 1} INTERSECT {A000040}.

EXAMPLE

a(1) = 7 = 3 + 5 - 1 where (3,5) is a twin prime pair.

a(2) = 11 = 5 + 7 - 1 where (5,7) is a twin prime pair.

MAPLE

P:=proc(n) local a, i; for i from 1 by 1 to n do if ithprime(i+1)-ithprime(i)=2 then a:=ithprime(i+1)+ithprime(i)-1; if isprime(a) then print(a); fi; fi; od; end: P(300); # Paolo P. Lava, Dec 21 2007

MATHEMATICA

lst={}; d=2; Do[p1=Prime[n]; p2=Prime[n+1]; p=p1+p2-1; If[PrimeQ[p]&&p2-p1==d, AppendTo[lst, p]], {n, 10^3}]; lst (* Vladimir Joseph Stephan Orlovsky, Aug 14 2008 *)

Select[(Total[#]-1)&/@Select[Partition[Prime[Range[500]], 2, 1], Last[#]- First[#]== 2&], PrimeQ]  (* Harvey P. Dale, Apr 04 2011 *)

PROG

(PARI) is(p)=isprime((p-1)\2)&&isprime((p+3)\2)&&isprime(p) \\ Charles R Greathouse IV, Apr 18 2013

CROSSREFS

Cf. A000040, A001359, A005384, A006512, A054735.

Sequence in context: A111671 A213895 A140111 * A141305 A243916 A181841

Adjacent sequences:  A118069 A118070 A118071 * A118073 A118074 A118075

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 11 2006

EXTENSIONS

More terms from Harvey P. Dale, Apr 04 2011

STATUS

approved

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Last modified December 13 19:20 EST 2017. Contains 295976 sequences.