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

Author

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

Keywords

• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

Cf. A096215.

Programs

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]);

Mathematica

Select[Partition[Prime[Range[200]],2,1],PrimeQ[Total[#]+NextPrime[Total[#],-1]]&][[;;,1]] (* Harvey P. Dale, Dec 11 2024 *)