login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A138396 Primes n such that the left prime neighbors p1, p2 of n as well as the right prime neighbors q1, q2 of n form twin prime pairs and the sum p1+p2+n+q1+q2 is also prime. 1
37, 67, 277, 1297, 1307, 1613, 2099, 2333, 3533, 3571, 5507, 8849, 9029, 10061, 10289, 13697, 14621, 17203, 18013, 18127, 22613, 23053, 28559, 30859, 37357, 39233, 47407, 47681, 49537, 49999, 53239, 55639, 58379, 67421, 68863, 70937 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Might be called penta-primes.

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

The left prime neighbors 29, 31 of prime 37 and the right prime neighbors 41, 43 of 37 form twin prime pairs, and the sum 29+31+37+41+43 = 181 is prime. Hence 37 is in the sequence.

MATHEMATICA

a={}; Do[p0=Prime[n]; a1=Prime[n-2]; a2=Prime[n-1]; b1=Prime[n+1]; b2=Prime[n+2]; sp=a1+a2+p0+b1+b2; If[PrimeQ[sp]&&a2-a1==2&&b2-b1==2, AppendTo[a, p0]], {n, 3, 10^3}]; a

Select[Partition[Prime[Range[8000]], 5, 1], #[[2]]-#[[1]]==#[[5]]-#[[4]] == 2 && PrimeQ[Total[#]]&][[All, 3]] (* Harvey P. Dale, Oct 01 2017 *)

PROG

(MAGMA) P:= PrimesUpTo(71000); [ n: k in [3..#P-2] | p2-p1 eq 2 and q2-q1 eq 2 and IsPrime(p1+p2+n+q1+q2) where p1 is P[k-2] where p2 is P[k-1] where n is P[k] where q1 is P[k+1] where q2 is P[k+2] ]; // Klaus Brockhaus, Dec 04 2009

CROSSREFS

Cf. A001097 (twin primes).

Sequence in context: A063461 A105462 A119381 * A155087 A171807 A178399

Adjacent sequences:  A138393 A138394 A138395 * A138397 A138398 A138399

KEYWORD

nonn

AUTHOR

Vladimir Joseph Stephan Orlovsky, May 08 2008

EXTENSIONS

More terms from Vladimir Joseph Stephan Orlovsky, Dec 17 2008

Edited by Klaus Brockhaus, Dec 04 2009

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 13:50 EST 2019. Contains 329877 sequences. (Running on oeis4.)