A355484 - OEIS

%I #10 Jul 11 2022 13:26:33

%S 1,6,9,21,17,33,45,51,75,99,111,93,105,135,153,201,165,249,231,237,

%T 321,225,273,363,411,393,285,315,471,483,435,405,465,555,681,495,783,

%U 675,873,849,963,1729,585,525,897,795,1041,915,735,855,1191,825,765,1095,975,1005,1035,1125,1311,1407

%N a(n) is the least positive number that can be represented in exactly n ways as 2*p+q where p and q are primes.

%C a(n) is the least number k such that A046926(k) = n.

%H Robert Israel, <a href="/A355484/b355484.txt">Table of n, a(n) for n = 0..2500</a>

%e a(3) = 21 because 21 can be written as 2*p+q with p and q prime in exactly 3 ways, namely 21 = 2*2+17 = 2*5+11 = 2*7+7, and no smaller number works.

%p M:= 3000: # to use primes up to M

%p P:= select(isprime,[2,seq(i,i=3..M,2)]): nP:= nops(P):

%p A:= Vector(M):

%p for i from 1 do

%p   p:= P[i];

%p   if 2*p >= M then break fi;

%p   for j from 1 to nP do

%p     q:= P[j];

%p     v:= 2*p+q;

%p     if v > M then break fi;

%p     A[v]:= A[v]+1;

%p od od:

%p K:= max(A):

%p V:= Array(0..K+1):

%p for i from 1 to M do

%p   if V[A[i]] = 0 then V[A[i]]:= i fi

%p od:

%p L:= min(select(t -> V[t] = 0, [$1..K+1])):

%p convert(V[0..L-1],list);

%Y Cf. A046926, A284052.

%K nonn

%O 0,2

%A _J. M. Bergot_ and _Robert Israel_, Jul 03 2022