A103852 Numbers n such that 2*P(n)+1, 2*P(n+1)+1, and 2*P(n+2)-1 are also consecutive primes with P(n+1)=P(n)+6 and P(n+2)=P(n+1)+2 with P(i)=i-th prime.

119, 372, 814, 4350, 9797, 16625, 16729, 48121, 63137, 71520, 83264, 103551, 111283, 113690, 232363, 268661, 302024, 333947, 334725, 340910, 352997, 381169, 404828, 414097, 565240, 606243, 607228, 613165, 660386, 724426, 833947, 897951, 932125, 947360

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

Cf. A103851.

Sequence in context: A257603 A063348 A243581 * A157040 A256907 A049226

Adjacent sequences: A103849 A103850 A103851 * A103853 A103854 A103855

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