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

1,1

Comments

The Rivera link gives the first 15 terms.

Links

Table of n, a(n) for n=1..15.

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

Example

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.

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 *)

Crossrefs

Cf. A001043, A253969.

Sequence in context: A167735 A221517 A264247 * A360064 A067257 A134497

Adjacent sequences: A348575 A348576 A348577 * A348579 A348580 A348581

Keyword

nonn,more

Author

Michel Marcus, Oct 24 2021

Status

approved