A345316 a(n) is the first number k such that there are exactly n primes of the form k + A - B where A and B are sums of subsets of the prime factors of k.

1, 2, 39, 20, 6, 10, 105, 285, 165, 615, 570, 1482, 1596, 2706, 3885, 14790, 19470, 24090, 19425, 33630, 33558, 80178, 134178, 115878, 151662, 428090, 418938, 631470, 672105, 1366530, 1006278, 1461570, 1155990, 1718310, 2382510, 3344430, 3669090, 4441530, 4562922, 3545178, 6087030, 7945230

Offset

0,2

Links

Table of n, a(n) for n=0..41.

Formula

A345300(a(n)) = n.

Example

a(3) = 20 because there are exactly 3 primes of this form for k=20, namely 13 = 20-2-5, 17 = 20+2-5, and 23 = 20+5-2, and this is the least number for which there are exactly 3 such primes.

Maple

f:= proc(n) local S, p;
  S:= {n};
  for p in numtheory:-factorset(n) do
    S:= S union map(`+`, S, p) union map(`-`, S, p)
  od:
  nops(select(isprime, S))
end proc:
V:= Array(0..30): count:= 0:
for n from 1 while count < 31 do
v:= f(n);
if v <= 30 and V[v] = 0 then count:= count+1; V[v]:= n fi
od:
convert(V, list);

Crossrefs

Cf. A345300.

Sequence in context: A263374 A066244 A055689 * A028442 A062982 A042801

Adjacent sequences: A345313 A345314 A345315 * A345317 A345318 A345319

Keyword

nonn

Author

J. M. Bergot and Robert Israel, Jun 13 2021

Status

approved