A329165 Let P1, P2, P3, P4 be consecutive primes with P2-P1=P4-P3=2. a(n)=(P3-P1)/6 when the length of the gap with no primes between the two pairs of twin primes sets a record.

1, 2, 3, 5, 6, 9, 12, 17, 18, 21, 22, 23, 25, 31, 33, 35, 40, 41, 42, 47, 48, 49, 51, 52, 53, 57, 58, 62, 63, 66, 71, 75, 77, 78, 81, 83, 85, 90, 91, 93, 98, 100, 105, 108, 111, 115, 119, 123, 125, 135, 138, 148, 150, 152, 165, 170, 173, 180

Offset: 1

Author

Hugo Pfoertner, Nov 07 2019

Keywords

• nonn
• more

Comments

The position of the occurrence of the n-th record is given by A329164(n)=(P1+P2)/12.

Examples

			See A329164.
		

Crossrefs

Cf. A053778, A329158, A329159, A329160, A329161, A329164.

Programs

Mathematica

With[{s = Partition[Prime@ Range[10^5], 4, 1]}, Union@ FoldList[Max, Map[(#3 - #1)/6 & @@ # &, Select[s, #2 - #1 == #4 - #3 == 2 & @@ # &]]]] (* Michael De Vlieger, May 26 2020 *)

PARI

p1=3;p2=5;p3=7;r=0;forprime(p4=11,1e9,if(p2-p1==2&&p4-p3==2,d=p3-p1;if(d>r,r=d;print1(d/6,", ")));p1=p2;p2=p3;p3=p4)

Extensions

a(27)-a(28) from Jinyuan Wang, Mar 01 2020

a(29)-a(58) found by Tomáš Brada, Natalia Makarova, May 12 2020