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

0,1

Comments

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

Links

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

Example

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.

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);

Crossrefs

Cf. A072511, A356864.

Sequence in context: A227456 A214429 A002382 * A330856 A180384 A023168

Adjacent sequences: A356475 A356476 A356477 * A356479 A356480 A356481

Keyword

nonn

Author

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

Status

approved