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A067187 Numbers that can be expressed as the sum of two primes in exactly one way. 17

%I #23 Mar 10 2022 10:38:15

%S 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 85,91,99,103,105,109,111,115,129,133,139,141,151,153,159,165,169,175,

%U 181,183,193,195,199,201,213,225,229,231,235,241,243,253,259,265,271

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

%C All primes + 2 are terms of this sequence. Is 12 the last even term? - _Frank Ellermann_, Jan 17 2002

%C A048974, A052147, A067187 and A088685 are very similar after dropping terms less than 13. - _Eric W. Weisstein_, Oct 10 2003

%C Values of n such that A061358(n)=1. - _Emeric Deutsch_, Apr 03 2006

%H <a href="/index/Go#Goldbach">Index entries for sequences related to Goldbach conjecture</a>

%e 4 is a term as 4 = 2+2, 15 is a term as 15 = 13+2.

%p 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 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 *)

%Y Cf. A023036, A045917, A061358.

%Y Subsequence of A014091.

%Y 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 nonn

%O 1,1

%A _Amarnath Murthy_, Jan 10 2002

%E Edited by _Frank Ellermann_, Jan 17 2002

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)