cp's OEIS Frontend

A258713 A001172(n)/2: Least k such that 2k is a sum of two odd primes in exactly n ways.

%I A258713 #18 Nov 15 2023 15:57:55
%S A258713 0,3,5,11,17,24,30,39,42,45,57,72,60,84,90,117,123,144,120,105,162,
%T A258713 150,180,237,165,264,288,195,231,240,210,285,255,336,396,378,438,357,
%U A258713 399,345,519,315,504,465,390,480,435,462,450,567,717,420,495,651
%N A258713 A001172(n)/2: Least k such that 2k is a sum of two odd primes in exactly n ways.
%C A258713 Up to a(14) also indices of records in A002375, number of ways to write 2n as sum of two odd primes. - _M. F. Hasler_, Aug 21 2017
%H A258713 Robert Israel, <a href="/A258713/b258713.txt">Table of n, a(n) for n = 0..845</a>
%p A258713 g:= add(x^ithprime(i),i=2..1000):
%p A258713 G:= series((g^2+add(x^(2*ithprime(i)),i=2..1000))/2,x,ithprime(1001)+3):
%p A258713 A[0]:= 0:
%p A258713 for k from 1 to (ithprime(1001)+1)/2 do
%p A258713   m:= coeff(G,x,2*k);
%p A258713   if not assigned(A[m]) then A[m]:= k fi;
%p A258713 od:
%p A258713 for m from 1 while assigned(A[m]) do od:
%p A258713 seq(A[i],i=0..m-1); # _Robert Israel_, Aug 21 2017
%t A258713 With[{s = Array[Count[Select[IntegerPartitions[2 #, 2], Length@ # == 2 &], p_ /; AllTrue[p, And[PrimeQ@ #, OddQ@ #] &]] &, 10^3]}, Table[FirstPosition[s, n][[1]] /. 1 -> 0, {n, 0, 53}]] (* _Michael De Vlieger_, Aug 21 2017 *)
%Y A258713 Cf. A136244, A001172.
%Y A258713 Cf. A002375, A002372, A045917.
%K A258713 nonn
%O A258713 0,2
%A A258713 _N. J. A. Sloane_, Jun 14 2015
%E A258713 Edited by _M. F. Hasler_, Aug 21 2017
%E A258713 Edited by _Robert Israel_, Aug 21 2017