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 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. 1
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified December 1 23:26 EST 2023. Contains 367503 sequences. (Running on oeis4.)