A347079 a(n) is the least prime that is the perimeter of exactly n isosceles triangles with prime sides.

2, 7, 17, 41, 89, 149, 229, 281, 461, 401, 557, 761, 941, 929, 1061, 1049, 1321, 1409, 1747, 1721, 1901, 2131, 2237, 2647, 2531, 2609, 3203, 3217, 3089, 3209, 3257, 3607, 3739, 4129, 4733, 4549, 4721, 4637, 5441, 4817, 5557, 5689, 5393, 6379, 6977, 6857, 7393, 7253, 6961, 7451, 7901, 7561, 8609

Offset

0,1

Comments

a(n) is the least prime p such that there are exactly n pairs of primes (q,r) with 2*q+r = p and r < 2*q.

Links

Robert Israel, Table of n, a(n) for n = 0..808

Example

a(3) = 41 because 41 is prime and there are exactly 3 such triangles with perimeter 41, namely with sides (19,19,3), (17,17,7) and (11,11,19).

Maple

N:= 10000: # for terms before the first term > N
V:= Vector(N):
p:= 1;
do
  p:= nextprime(p);
  if 2*p >= N then break fi;
  q:= floor(p/2);
  do
      q:= nextprime(q);
      r:= 2*q+p;
      if r > N then break fi;
      if isprime(r) then V[r]:= V[r]+1 fi;
  od
od:
m:= max(V):
A:= Array(0..m):
A[0]:= 2:
for n from 3 to N by 2 do
if A[V[n]] = 0 then A[V[n]]:= n fi
od:
L:= convert(A, list):
if member(0, L, 'm') then L[1..m-1] else L fi;

Mathematica

f[p_] := Count[Select[Range[(p - 1)/2], PrimeQ], _?(PrimeQ[(p - #)/2] &)]; v = f /@ (p = Select[Range[10000], PrimeQ]); p[[TakeWhile[Table[FirstPosition[v, k][[1]], {k, 0, Max[v]}], NumericQ]]] (* Amiram Eldar, Aug 17 2021 *)

Crossrefs

Sequence in context: A364756 A175660 A365069 * A370304 A175120 A239357

Adjacent sequences: A347076 A347077 A347078 * A347080 A347081 A347082

Keyword

nonn

Author

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

Status

approved