A356478 a(n) is the least k such that there are exactly n primes p <= k such that 2*k-p and p*(2*k-p)+2*k are also prime.

2, 4, 11, 15, 21, 35, 42, 111, 81, 117, 126, 60, 291, 147, 225, 417, 210, 330, 357, 555, 561, 375, 315, 477, 735, 552, 420, 975, 630, 585, 816, 840, 930, 1925, 1302, 1170, 1140, 2202, 1215, 1155, 1911, 1551, 2031, 1590, 1365, 2136, 1425, 2562, 1740, 1485, 2331, 2790, 2160, 2100, 2640, 2010, 3681, 2400, 1785, 2262, 3252, 2622, 2940, 1575, 2310, 2541, 3987, 2772

Offset: 0

Author

J. M. Bergot and Robert Israel, Sep 01 2022

Keywords

• nonn

Comments

a(n) is the least k such that A356864(k) = n.

Examples

			a(3) = 15 because there are exactly 3 primes p <= 15 with 30-p and p*(30-p)+30 prime, namely 7, 11 and 13, and no smaller number works.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A072511, A356864.

Programs

Maple

f:= proc(n) local p,q,t;
  p:= 1: t:= 0:
  do
    p:= nextprime(p);
    q:= n-p;
    if q <= p then return t fi;
    if isprime(q) and isprime(p*q+n) then t:= t+1 fi;
  od
end proc:
V:= Array(0..100): V[0]:= 2: count:= 1:
for nn from 2 while count < 101 do
  v:= f(2*nn);
  if v > 100 then next fi;
  if V[v] = 0 then count:= count+1; V[v]:= nn; fi;
od:
convert(V,list);