A346416 Primes p such that the greatest perimeter of a triangle with prime sides including p and the next prime is prime.

5, 11, 13, 17, 19, 37, 41, 43, 47, 59, 71, 89, 103, 109, 113, 137, 139, 149, 163, 167, 173, 179, 181, 241, 269, 313, 337, 379, 389, 401, 491, 499, 521, 547, 557, 569, 587, 599, 607, 613, 617, 631, 643, 673, 677, 701, 739, 773, 787, 811, 839, 877, 883, 887, 929, 941, 953, 971, 977, 983, 1019, 1021

Offset

1,1

Comments

If p is prime and q is the next prime, the greatest perimeter is p+q+r where r is the greatest prime < p+q.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(3) = 13 is a term because the next prime is 17, the greatest prime < 13+17 is 29, and 13+17+29 = 59 is prime.

Maple

f:= proc(n) local p, q, r, s;
  p:= ithprime(n);
  q:= ithprime(n+1);
  r:= prevprime(p+q);
  s:= p+q+r;
  if isprime(p+q+r) then return p fi
end proc:
map(f, [$1..500]);

Crossrefs

Cf. A096215.

Sequence in context: A090320 A085909 A288450 * A371449 A272446 A307390

Adjacent sequences: A346413 A346414 A346415 * A346417 A346418 A346419

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 15 2021

Status

approved