A284052 Smallest prime representable in exactly n ways as p + 2*q, p and q primes.

7, 11, 23, 17, 41, 97, 89, 113, 163, 197, 257, 233, 373, 317, 389, 491, 613, 557, 641, 773, 761, 953, 977, 929, 1097, 1049, 1109, 1217, 1433, 1327, 1493, 1613, 1553, 1871, 1759, 1877, 1747, 2003, 2357, 2287, 2237, 2213

Offset

1,1

Comments

The sequence is non-monotone and infinite.

Links

Robert Israel, Table of n, a(n) for n = 1..2000

Example

7 = 3 + 2*2,
11 = 7 + 2*2 = 5 + 2*3,
23 = 13 + 2*5 = 17 + 2*3 = 19 + 2*2,
17 = 3 + 2*7 = 7 + 2*5 = 11 + 2*3 = 13 + 2*2.

Maple

N:= 10000: # for all terms before the first term > N
V:= Vector(N):
Primes:= select(isprime, [2, seq(i, i=3..N, 2)]):
for ip from 1 to nops(Primes) do
  p:= Primes[ip];
  for iq from 1 do
    r:= p+2*Primes[iq];
    if r > N then break fi;
    V[r]:= V[r]+1;
od od:
Nmax:= max(V):
A:= Vector(Nmax):
for p in Primes do
  m:= V[p];
  if m > 0 and A[m] = 0 then A[m]:= p fi;
od:
m:= min(select(t -> A[t]=0, [$1..Nmax])):
seq(A[i], i=1..m-1); # Robert Israel, Jun 07 2020

Mathematica

np[n_] := np[n] = Length@ Select[n - 2*Prime@ Range@ PrimePi[n/2], PrimeQ]; a[n_] := Block[{p=2}, While[np[p] != n, p = NextPrime@ p]; p]; Array[a, 100] (* Giovanni Resta, Mar 19 2017 *)

Crossrefs

Sequence in context: A175651 A372045 A362979 * A211433 A039511 A103667

Adjacent sequences: A284049 A284050 A284051 * A284053 A284054 A284055

Keyword

nonn

Author

Zak Seidov, Mar 19 2017

Status

approved