A138399 Ennea-Primes. Prime Numbers n (single prime number in-between 8 twin primes) such that Sum of 9 prime numbers (8 twin primes and single prime number in-between) are primes.

4253, 626617, 1841681, 2169007, 2484931, 9198577, 9600571, 16738861, 21240283, 21836767, 23121403, 23405593, 27437131, 31189801, 33615229, 36035029, 44275331, 57940061, 65499923, 79780271, 81630529, 83169227, 108246967, 111928343

Offset

1,1

Comments

{5 penta-} {9 ennea-} Table of non-technical numeric prefixes -- http://en.wikipedia.org/wiki/Numerical_prefix

Links

Table of n, a(n) for n=1..24.

Example

{4229,4231} {4241,4243} {4253} {4259,4261} {4271,4273} Sum = 38261.

Mathematica

a={}; Do[p0=Prime[n]; a1=Prime[n-4]; a2=Prime[n-3]; b1=Prime[n-2]; b2=Prime[n-1]; c1=Prime[n+1]; c2=Prime[n+2]; d1=Prime[n+3]; d2=Prime[n+4]; sp=a1+a2+b1+b2+p0+c1+c2+d1+d2; If[PrimeQ[sp]&&a2-a1==2&&b2-b1==2&&c2-c1==2&&d2-d1==2, AppendTo[a, p0]], {n, 5, 10^6}]; a
spn8Q[m_]:=Module[{d=Differences[m]}, PrimeQ[Total[m]]&&d[[1]] == d[[3]] == d[[6]] == d[[8]]==2]; Select[Partition[Prime[Range[650000]], 9, 1], spn8Q][[All, 5]] (* Harvey P. Dale, Aug 24 2016 *)

Crossrefs

Sequence in context: A205995 A237805 A031985 * A224725 A252030 A371569

Adjacent sequences: A138396 A138397 A138398 * A138400 A138401 A138402

Keyword

nonn,uned

Author

Vladimir Joseph Stephan Orlovsky, May 08 2008

Extensions

More terms from Harvey P. Dale, Aug 24 2016

Status

approved