A120397 Minimal number of steps needed to represent a prime >=5 as a sum of at most 3 primes such that all the previous odd primes are represented.

1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 10, 10, 11, 11, 11, 12, 13

Offset

1,2

Comments

This sequence contains probably every natural number, though this should be checked further. Conjecture: Every prime >=5 can be represented as a sum of at most 3 primes, such that all the previous odd primes are represented.

Links

Table of n, a(n) for n=1..25.

Example

5=2+3->1 step
7=2+2+3=2+5->2 steps
11=2+2+7=3+3+5->2 steps
13=2+11=3+5+5=3+3+7->3 steps
41=2+2+37=3+7+31=5+7+29=5+13+23=5+17+19=11+13+17->6 steps

Crossrefs

Sequence in context: A093337 A254528 A176044 * A104305 A050506 A155213

Adjacent sequences: A120394 A120395 A120396 * A120398 A120399 A120400

Keyword

nonn

Author

Robin Garcia, Jul 01 2006

Status

approved