A347259 a(n) is the least prime that can be written in exactly n ways as s+2*p where s is a semiprime and p is a prime, or 0 if no such prime exists.

2, 13, 19, 31, 43, 59, 61, 83, 127, 149, 151, 181, 257, 167, 241, 223, 251, 401, 227, 311, 419, 383, 347, 499, 479, 547, 631, 593, 523, 599, 563, 727, 691, 743, 857, 829, 953, 863, 853, 827, 1093

Offset

0,1

Comments

a(41) > 10^5 if it is not 0.

Conjecture: First zeros of the sequence are a(41), a(666), a(1277), a(2701), ... - Giorgos Kalogeropoulos, Sep 23 2021

Links

Table of n, a(n) for n=0..40.

Example

a(3) = 31 because the prime 31 can be obtained in exactly 3 ways:
31 = 9+2*11 = 21+2*5 = 25+2*3
and this is the least such prime.

Maple

N:= 10000: # to search values up to N
P:= select(isprime, [2, seq(i, i=3..N, 2)]):
S:= select(t -> numtheory:-bigomega(t)=2, [$1..N]):
V:= Vector(N):
for p in P do
  for s in S do
    r:= s+2*p;
    if r > N then break fi;
    V[r]:= V[r]+1
  od
od:
m:= min({$0..max(V[P])} minus convert(V[P], set))-1:
M:= Array(0..m):
for p in P do
v:= V[p];
  if v <= m and M[v] = 0 then M[v]:= p fi
od:
convert(M, list);

Mathematica

Table[k=2; While[Length@Select[k-2Prime@Range@PrimePi@Floor[k/2], PrimeOmega@#==2&]!=n, k=NextPrime@k]; k, {n, 0, 40}] (* Giorgos Kalogeropoulos, Sep 23 2021 *)

Crossrefs

Sequence in context: A067208 A142348 A309663 * A181686 A206462 A339542

Adjacent sequences: A347256 A347257 A347258 * A347260 A347261 A347262

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Aug 24 2021

Status

approved