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
Keywords
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
Programs
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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);
Comments