A348578 Primes that begin a record list of consecutive primes whose sum of any 2 consecutive terms is divisible by 3.

5, 89, 809, 3954889, 15186319, 77011289, 288413159, 62585146739, 114058236679, 143014298809, 2320700383121, 2942277160583, 4386778243843, 16104860854333, 23171469790747

Offset: 1

Author

Michel Marcus, Oct 24 2021

Keywords

• nonn
• more

Comments

The Rivera link gives the first 15 terms.

Examples

			A001043 begins as (5, 8, 12, 18, 24, 30, 36, 42, 52) where 7 consecutive terms are multiple of 3 starting at 3rd term, corresponding to 5=prime(3), so 5 is the 1st term of this sequence.
		

Links

• Carlos Rivera, Puzzle 1059 Set of consecutive primes such that..., The Prime Puzzles and Problems Connection.

Crossrefs

Cf. A001043, A253969.

Programs

Mathematica

p=2;t=r=0;Monitor[Do[p=NextPrime[p];t=0;While[Mod[p+NextPrime@p,3]==0,p=NextPrime@p;t++];If[t>r,Print[NextPrime[p,-t]];r=t],{n,10^14}],p] (* Giorgos Kalogeropoulos, Oct 24 2021 *)