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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.
0
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
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
KEYWORD
nonn,more
AUTHOR
J. M. Bergot and Robert Israel, Aug 24 2021
STATUS
approved