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

1,1

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

Links

Table of n, a(n) for n=1..60.

Index entries for sequences related to Goldbach conjecture

Example

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

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 *)

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).

Sequence in context: A321025 A047569 A039062 * A321353 A161674 A285623

Adjacent sequences: A067184 A067185 A067186 * A067188 A067189 A067190

Keyword

nonn

Author

Amarnath Murthy, Jan 10 2002

Extensions

Edited by Frank Ellermann, Jan 17 2002

Status

approved