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A339652 a(n) is the least number k such that 2*k+1 has exactly n expressions as p+2*q where p and q are primes, or 0 if there is no such k.

%I A339652 #19 Dec 15 2020 03:08:29
%S A339652 1,3,4,10,8,16,22,25,37,49,55,46,52,67,76,100,82,124,115,118,160,112,
%T A339652 136,181,205,196,142,157,235,241,217,202,232,277,340,247,391,337,436,
%U A339652 424,481,864,292,262,448,397,520,457,367,427,595,412,382,547,487,502,517,562,655,703,598,760,592
%N A339652 a(n) is the least number k such that 2*k+1 has exactly n expressions as p+2*q where p and q are primes, or 0 if there is no such k.
%C A339652 Conjecture: all a(n) > 0.
%H A339652 Robert Israel, <a href="/A339652/b339652.txt">Table of n, a(n) for n = 0..9400</a>
%F A339652 A046927(a(n)) = n if a(n) > 0.
%e A339652 a(4) = 8 because 2*8+1 = 17 has exactly 4 representations as p+2*q: 17 = 3 + 2*7 = 7 + 2*5 = 11 + 2*3 = 13 + 2*2, and this is not true for any k < 8.
%p A339652 # given table A046927
%p A339652 R:= Array(0..100):
%p A339652 for i from 0 to max(indices(A046927)) do
%p A339652   v:= A046927[i];
%p A339652   if R[v]= 0 then R[v]:= i fi
%p A339652 od:
%p A339652 seq(R[i],i=0..100);
%o A339652 (PARI) f(n) = my(s); n=2*n+1; forprime(p=2, n\2, s+=isprime(n-2*p)); s;
%o A339652 a(n) = my(k=1); while(f(k) != n, k++); k; \\ _Michel Marcus_, Dec 14 2020
%Y A339652 Cf. A046927, A339709.
%K A339652 nonn
%O A339652 0,2
%A A339652 _J. M. Bergot_ and _Robert Israel_, Dec 13 2020