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A347079
a(n) is the least prime that is the perimeter of exactly n isosceles triangles with prime sides.
1
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
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 A375821 A175120
KEYWORD
nonn
AUTHOR
J. M. Bergot and Robert Israel, Aug 15 2021
STATUS
approved