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

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, 85, 91, 99, 103, 105, 109, 111, 115, 129, 133, 139, 141, 151, 153, 159, 165, 169, 175, 181, 183, 193, 195, 199, 201, 213, 225, 229, 231, 235, 241, 243, 253, 259, 265, 271

Offset: 1

Author

Amarnath Murthy, Jan 10 2002

Keywords

• nonn

Comments

All primes + 2 are terms of this sequence. Is 12 the last even term? - Frank Ellermann, Jan 17 2002

A048974, A052147, A067187 and A088685 are very similar after dropping terms less than 13. - Eric W. Weisstein, Oct 10 2003

Values of n such that A061358(n)=1. - Emeric Deutsch, Apr 03 2006

Examples

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

Links

• Robert Price, Table of n, a(n) for n = 1..5002
• Index entries for sequences related to Goldbach conjecture

Crossrefs

Cf. A023036, A045917, A061358.

Subsequence of A014091.

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).

Programs

Maple

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

Mathematica

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 = 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 *)

Extensions

Edited by Frank Ellermann, Jan 17 2002