A355484 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.

1, 6, 9, 21, 17, 33, 45, 51, 75, 99, 111, 93, 105, 135, 153, 201, 165, 249, 231, 237, 321, 225, 273, 363, 411, 393, 285, 315, 471, 483, 435, 405, 465, 555, 681, 495, 783, 675, 873, 849, 963, 1729, 585, 525, 897, 795, 1041, 915, 735, 855, 1191, 825, 765, 1095, 975, 1005, 1035, 1125, 1311, 1407

Offset

0,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 0..2500

Example

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.

Maple

M:= 3000: # to use primes up to M
P:= select(isprime, [2, seq(i, i=3..M, 2)]): nP:= nops(P):
A:= Vector(M):
for i from 1 do
  p:= P[i];
  if 2*p >= M then break fi;
  for j from 1 to nP do
    q:= P[j];
    v:= 2*p+q;
    if v > M then break fi;
    A[v]:= A[v]+1;
od od:
K:= max(A):
V:= Array(0..K+1):
for i from 1 to M do
  if V[A[i]] = 0 then V[A[i]]:= i fi
od:
L:= min(select(t -> V[t] = 0, [$1..K+1])):
convert(V[0..L-1], list);

Crossrefs

Cf. A046926, A284052.

Sequence in context: A154783 A096546 A357840 * A358222 A165717 A239874

Adjacent sequences: A355481 A355482 A355483 * A355485 A355486 A355487

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jul 03 2022

Status

approved