A339709 a(n) is the least even number that has exactly n decompositions as the sum of an odd prime and a semiprime, or 0 if there is no such number.

2, 12, 20, 26, 28, 44, 38, 52, 76, 80, 62, 92

Offset

0,1

Comments

a(n) is the least even number 2*k such that A339708(k)=n.

Conjecture: a(12) = 0, but a(n) > 0 for all other n.

Since this is only a conjecture, the Data stops at a(11)=92.

For n>=13, the sequence continues with 98, 136, 128, 122, 158, 166, 152, 206, 188, 222, 242, 232, 248, 266, 272, 296, 320, 308, 352, 382, 412, 326, 418, 402, 440, 454, 398, 492, 458, 488, 500, 554, 542, 518, 578, 618, 572, 626, 642, 678, 632, ...

Links

Table of n, a(n) for n=0..11.

Robert Israel, Table of n, a(n) for n = 0 .. 800 (with conjectured a(12)=0).

Example

a(4) = 28 because we can write 28 = 3+25 = 7+21 = 13+15 = 19+9 where 3, 7, 13 and 19 are odd primes and 25, 21, 15, and 9 are semiprimes, and 28 is the least even number with exactly 4 decompositions of this type.

Maple

N:= 10000:
P:= select(isprime, [seq(i, i=3..N, 2)]):S:= sort(select(`<`, [seq(seq(P[i]*P[j], i=1..j), j=1..nops(P))], N)):V:= Vector(N):
for p in P do
  for s in S while p+s<=N do V[p+s]:= V[p+s]+1 od
od:R:= Array(0..max(V)):for i from 2 to N by 2 do
  v:= V[i];
  if R[v] = 0 then R[v]:= i fi
od:convert(R[1..500], list);

Crossrefs

Cf. A339708.

Sequence in context: A069164 A067762 A305162 * A137311 A032407 A136725

Adjacent sequences: A339706 A339707 A339708 * A339710 A339711 A339712

Keyword

nonn,more

Author

J. M. Bergot and Robert Israel, Dec 13 2020

Status

approved