A396527 a(n) is the least number that is the sum of two distinct upper twin primes in exactly n ways, or -1 if there is no such number.

12, 50, 116, 242, 290, 212, 704, 662, 1292, 1334, 2072, 1892, 2342, 3722, 3614, 2312, 3542, 4790, 4412, 6122, 4202, 3572, 5702, 5252, 6722, 5852, 6512, 8402, 10892, 8192, 6932, 10952, 10292, 11972, 10922, 14282, 11552, 16382, 17252, 17222, 18062, 16172, 18482, 13862, 20132, 17852, 16592, 23102, 22472, 28382, 24992, 29822, 28562, 21212

Offset

1,1

Comments

Conjecture: a(n) > 0 for all n.

Links

Robert Israel, Table of n, a(n) for n = 1..500

Example

a(3) = 116 because 116 = 7 + 109 = 13 + 103 = 43 + 73 is the sum of two upper twin primes in exactly 3 ways, and no smaller number works.

Maple

N:= 60: V:= Vector(N): V[1]:= 12: count:= 1:
P:= select(t -> isprime(t) and isprime(t-2), [seq(i, i=7..10^5, 6)]):
for k from 14 by 6 to 10^5 while count < N do
  t:= 0:
  for i from 1 do
    q:= k - P[i];
    if q <= P[i] then break fi;
    if member(q, P) then t:= t+1 fi;
  od;
  if t >= 2 and t <= N and V[t] = 0 then V[t]:= k; count:= count+1;  fi
od:
convert(V, list);

Crossrefs

Cf. A006512, A334160, A396487.

Sequence in context: A009930 A066644 A009934 * A009927 A009938 A063491

Adjacent sequences: A396524 A396525 A396526 * A396528 A396530 A396531

Keyword

nonn

Author

Robert Israel, May 28 2026

Status

approved