1,2

At least for the first 200 primes, it is true that every prime p>2 can be expressed as 2*(p1-p2) + 3*p3, where p1, p2, p3 are primes or 1, less than or equal than p (the proof would be straightforward if both a)levy's conjecture and b) the conjecture saying that every prime p>3 can be expressed as 2*p1 + 3*p2, where p1, p2 are primes, were true). It would be interesting to study how the sequence changes, when we remove the restriction for p1, p2, p3 to be less than or equal than p.

a(12)=30 because 37 (the 12th prime)can be expressed as

2*( 1 - 2 ) + 3* 13

OR 2*( 1 - 11 ) + 3* 19

OR 2*( 1 - 17 ) + 3* 23

OR 2*( 1 - 29 ) + 3* 31

OR 2*( 2 - 3 ) + 3* 13

OR 2*( 3 - 1 ) + 3* 11

OR 2*( 3 - 13 ) + 3* 19

OR 2*( 3 - 19 ) + 3* 23

OR 2*( 3 - 31 ) + 3* 31

OR 2*( 5 - 3 ) + 3* 11

OR 2*( 7 - 5 ) + 3* 11

OR 2*( 7 - 17 ) + 3* 19

OR 2*( 7 - 23 ) + 3* 23

OR 2*( 11 - 3 ) + 3* 7

OR 2*( 13 - 2 ) + 3* 5

OR 2*( 13 - 5 ) + 3* 7

OR 2*( 13 - 11 ) + 3* 11

OR 2*( 13 - 23 ) + 3* 19

OR 2*( 13 - 29 ) + 3* 23

OR 2*( 17 - 3 ) + 3* 3

OR 2*( 19 - 2 ) + 3* 1

OR 2*( 19 - 5 ) + 3* 3

OR 2*( 19 - 11 ) + 3* 7

OR 2*( 19 - 17 ) + 3* 11

OR 2*( 19 - 29 ) + 3* 19

OR 2*( 31 - 17 ) + 3* 3

OR 2*( 31 - 23 ) + 3* 7

OR 2*( 31 - 29 ) + 3* 11

OR 2*( 37 - 23 ) + 3* 3

OR 2*( 37 - 29 ) + 3* 7

Sequence in context: A077025 A032729 A035270 this_sequence A060428 A035238 A003136

Adjacent sequences: A120448 A120449 A120450 this_sequence A120452 A120453 A120454

nonn

Vassilis Papadimitriou (bpapa(AT)sch.gr), Jul 20 2006