A067188 Numbers that can be expressed as the (unordered) sum of two primes in exactly two ways.

10, 14, 16, 18, 20, 28, 32, 38, 68

Offset

1,1

Comments

Corresponds to numbers 2m such that A045917(m)=2. Subsequence of A014091. - Lekraj Beedassy, Apr 22 2004

Links

Table of n, a(n) for n=1..9.

Index entries for sequences related to Goldbach conjecture

Example

18 is a term as 18 = 13+5 = 11+7 are the only two ways to express 18 as a sum of two primes.

Crossrefs

Cf. A023036.

Numbers that can be expressed as the sum of two primes in k ways for k=0..10: A014092 (k=0), A067187 (k=1), this sequence (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: A154774 A162708 A330210 * A092632 A213310 A055197

Adjacent sequences: A067185 A067186 A067187 * A067189 A067190 A067191

Keyword

nonn,fini,full

Author

Amarnath Murthy, Jan 10 2002

Extensions

Corrected by Peter Bertok (peter(AT)bertok.com), who finds (Jan 13 2002) that there are no other terms below 10000 and conjectures there are no further terms in this sequence and A067189, A067190, etc.

R. K. Guy (Jan 14 2002) remarks: "I believe that these conjectures follow from a more general one by Hardy & Littlewood (probably in Some problems of 'partitio numerorum' III, on the expression of a number as a sum of primes, Acta Math. 44(1922) 1-70)."

Status

approved