A345316 - OEIS

%I #5 Jun 14 2021 10:00:25

%S 1,2,39,20,6,10,105,285,165,615,570,1482,1596,2706,3885,14790,19470,

%T 24090,19425,33630,33558,80178,134178,115878,151662,428090,418938,

%U 631470,672105,1366530,1006278,1461570,1155990,1718310,2382510,3344430,3669090,4441530,4562922,3545178,6087030,7945230

%N 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.

%F A345300(a(n)) = n.

%e 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.

%p f:= proc(n) local S, p;

%p   S:= {n};

%p   for p in numtheory:-factorset(n) do

%p     S:= S union map(`+`, S, p) union map(`-`, S, p)

%p   od:

%p   nops(select(isprime, S))

%p end proc:

%p V:= Array(0..30): count:= 0:

%p for n from 1 while count < 31 do

%p v:= f(n);

%p if v <= 30 and V[v] = 0 then count:= count+1; V[v]:= n fi

%p od:

%p convert(V,list);

%Y Cf. A345300.

%K nonn

%O 0,2

%A _J. M. Bergot_ and _Robert Israel_, Jun 13 2021