A066722 Numbers that can be expressed as the sum of two primes in exactly six ways.

60, 66, 72, 100, 106, 110, 116, 118, 134, 146, 166, 172, 182, 212, 248, 332

Offset

1,1

Comments

No other terms below 10000. I conjecture 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)."

Links

Table of n, a(n) for n=1..16.

Index entries for sequences related to Goldbach conjecture

Mathematica

y = Select[Flatten@Table[Prime[i] + Prime[ j], {i, 500}, {j, 1, i}], # < Prime[500] &]; Select[Union[y], Count[y, #] == 6 &] (* Robert Price, Apr 22 2025 *)

Crossrefs

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), A067190 (k=4), A067191 (k=5), this sequence (k=6), A352229 (k=7), A352230 (k=8), A352231 (k=9), A352233 (k=10).

Sequence in context: A295697 A138690 A118155 * A080862 A239415 A106130

Adjacent sequences: A066719 A066720 A066721 * A066723 A066724 A066725

Keyword

nonn

Author

Peter Bertok (peter(AT)bertok.com), Jan 13 2002

Status

approved