login
A067190
Numbers that can be expressed as the sum of two primes in exactly four ways.
12
34, 36, 42, 46, 50, 58, 80, 88, 92, 122, 152
OFFSET
1,1
EXAMPLE
36 is a term as 36 = 31 + 5 = 29 + 7 = 23 + 13 = 19 + 17 are all the four ways to express 36 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), A067188 (k=2), A067189 (k=3), this sequence (k=4), A067191 (k=5), A066722 (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).
Sequence in context: A257315 A045561 A294282 * A306119 A218006 A345510
KEYWORD
nonn,fini,full
AUTHOR
Amarnath Murthy, Jan 10 2002
EXTENSIONS
Extended 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 A067188, A067189, etc.
R. K. Guy (Jan 14 2002) remarks: "I believe that these conjectures follow from a more general one by Hardy and 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