A341271 - OEIS

%I #9 Feb 15 2021 01:58:32

%S 16,18,16,36,34,34,48,46,46,66,64,76,108,64,64,108,104,76,144,106,110,

%T 144,106,106,156,112,112,186,142,142,198,154,154,234,154,154,276,184,

%U 184,246,196,230,318,184,184,288,202,196,318,232,232,318,244,244,354,274,232,354,244,244,426,274

%N a(n) is the least k such that there are distinct primes p,q,r,s such that k-p, k-q, k-r, k-s are primes and (p+q)/(r+s) = n.

%H Robert Israel, <a href="/A341271/b341271.txt">Table of n, a(n) for n = 1..249</a>

%e a(4) = 36 because 4 = (17+31)/(5+7) where 17,31,5,7 are primes and 36-17 = 19, 36-31 = 5, 36-5 = 31 and 36-7 = 29 are primes, and 36 is the least number k for which such primes exist.

%p f:= proc(n) local P,i,c1,c2;

%p   P:= select(t -> isprime(t) and isprime(n-t), {seq(i,i=3..n,2)});

%p   select(type,{seq(seq(convert(c1,`+`)/convert(c2,`+`), c1 = combinat:-choose(P minus c2,2)),c2 = combinat:-choose(P,2))},integer)

%p end proc:

%p N:= 70: # for a(1)..a(N)

%p V:= Vector(N): count:= 0:

%p for n from 2 by 2 while count < N do

%p   for v in f(n) do

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

%p od od:

%p convert(V,list);

%K nonn

%O 1,1

%A _J. M. Bergot_ and _Robert Israel_, Feb 07 2021