OFFSET
1,1
COMMENTS
3 consecutive primes with gaps 6 and 2 give 3 larger consecutive primes with gaps 12 and 2; the last two primes are twins, and the first two primes -- P(n) and P(n+1) -- are Sophie Germain primes.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..500
EXAMPLE
P(119)=653, P(120)=659, P(121)=661, 653+6=659, 659+2=661 2*653+1=1307, 2*659+1=1319, 2*661-1=1321; 1307, 1319, 1321 are consecutive primes so 119 is in the sequence.
MATHEMATICA
cpQ[{a_, b_, c_}]:=Module[{d=2a+1, e=2b+1, f=2c-1}, b-a==6&&c-b==2&& PrimeQ[ d] &&NextPrime[d]==e&&PrimeQ[f]]; PrimePi/@Select[Partition[ Prime[ Range[ 415000]], 3, 1], cpQ][[All, 1]] (* Harvey P. Dale, May 06 2018 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Pierre CAMI, Feb 18 2005
EXTENSIONS
Corrected, more terms from, and comment modified by Harvey P. Dale, May 06 2018
STATUS
approved