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A118071 Primes which are the sum of a twin prime pair + 1. 5
13, 37, 61, 277, 397, 457, 541, 1201, 1237, 1321, 1621, 1657, 2557, 2857, 3217, 4057, 4177, 4261, 4621, 5101, 5581, 6337, 6661, 6781, 7057, 7537, 8101, 8317, 8461, 8521, 8677, 9277, 9601, 10837, 10957, 11317, 11701, 12541, 12601, 12721, 13381, 13921 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Subset of A092738. - Paolo P. Lava, Dec 21 2007

Primes of the form 2*greater of twin primes-1. - Juri-Stepan Gerasimov, Apr 26 2010

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)

FORMULA

{A001359(k) + A006512(k) + 1} INTERSECT {A000040}.

{A054735(k) + 1} INTERSECT {A000040}.

{2*A001359(k) + 3} INTERSECT {A000040}.

{2*A006512(k) - 1} INTERSECT {A000040}. - Juri-Stepan Gerasimov, Apr 26 2010

EXAMPLE

a(1) = 13 = 5 + 7 + 1 where (5,7) is a twin prime pair.

a(2) = 37 = 17 + 19 + 1.

a(3) = 61 = 29 + 31 + 1.

a(4) = 277 = 137 + 139 + 1.

a(5) = 397 = 197 + 199 + 1.

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/@Select[Partition[Prime[Range[1000]], 2, 1], #[[2]]-#[[1]] == 2&]+1, PrimeQ] (* Harvey P. Dale, Jul 25 2019 *)

PROG

(PARI) is(n)=n%12==1 && isprime(n) && isprime(n\2-1) && isprime(n\2+1) \\ Charles R Greathouse IV, Jan 21 2015

CROSSREFS

Cf. A000040, A001359, A006512, A054735.

Sequence in context: A034938 A139530 A138368 * A307192 A147207 A146877

Adjacent sequences: A118068 A118069 A118070 * A118072 A118073 A118074

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, May 11 2006

EXTENSIONS

More terms added by Vladimir Joseph Stephan Orlovsky, Mar 10 2009

STATUS

approved

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Last modified November 28 00:05 EST 2022. Contains 358406 sequences. (Running on oeis4.)