cp's OEIS Frontend

A067187 Numbers that can be expressed as the sum of two primes in exactly one way.

%I A067187 #27 Apr 21 2025 17:08:45
%S A067187 4,5,6,7,8,9,12,13,15,19,21,25,31,33,39,43,45,49,55,61,63,69,73,75,81,
%T A067187 85,91,99,103,105,109,111,115,129,133,139,141,151,153,159,165,169,175,
%U A067187 181,183,193,195,199,201,213,225,229,231,235,241,243,253,259,265,271
%N A067187 Numbers that can be expressed as the sum of two primes in exactly one way.
%C A067187 All primes + 2 are terms of this sequence. Is 12 the last even term? - _Frank Ellermann_, Jan 17 2002
%C A067187 A048974, A052147, A067187 and A088685 are very similar after dropping terms less than 13. - _Eric W. Weisstein_, Oct 10 2003
%C A067187 Values of n such that A061358(n)=1. - _Emeric Deutsch_, Apr 03 2006
%H A067187 Robert Price, <a href="/A067187/b067187.txt">Table of n, a(n) for n = 1..5002</a>
%H A067187 <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>
%e A067187 4 is a term as 4 = 2+2, 15 is a term as 15 = 13+2.
%p A067187 g:=sum(sum(x^(ithprime(i)+ithprime(j)),i=1..j),j=1..80): gser:=series(g,x=0,280): a:=proc(n) if coeff(gser,x^n)=1 then n else fi end: seq(a(n),n=1..272); # _Emeric Deutsch_, Apr 03 2006
%t A067187 cQ[n_]:=Module[{c=0},Do[If[PrimeQ[n-i]&&PrimeQ[i],c++],{i,2,n/2}]; c==1]; Select[Range[4,271],cQ[#]&] (* _Jayanta Basu_, May 22 2013 *)
%t A067187 y = Select[Flatten@Table[Prime[i] + Prime[j], {i, 60}, {j, 1, i}], # < Prime[60] &]; Select[Union[y], Count[y, #] == 1 &] (* _Robert Price_, Apr 21 2025 *)
%Y A067187 Cf. A023036, A045917, A061358.
%Y A067187 Subsequence of A014091.
%Y A067187 Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), this sequence (k=1), A067188 (k=2), A067189 (k=3), A067190 (k=4), A067191 (k=5), A066722 (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).
%K A067187 nonn
%O A067187 1,1
%A A067187 _Amarnath Murthy_, Jan 10 2002
%E A067187 Edited by _Frank Ellermann_, Jan 17 2002