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%I #2 Mar 31 2012 20:08:02
%S 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
%N 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.
%C 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.
%e 5=2+3->1 step
%e 7=2+2+3=2+5->2 steps
%e 11=2+2+7=3+3+5->2 steps
%e 13=2+11=3+5+5=3+3+7->3 steps
%e 41=2+2+37=3+7+31=5+7+29=5+13+23=5+17+19=11+13+17->6 steps
%K nonn
%O 1,2
%A _Robin Garcia_, Jul 01 2006