Bad terms in sequence A108719?
Tautócrona
tautocrona at terra.es
Mon Nov 14 03:06:57 CET 2005
Sequence A108719 says:
5,7,13,17,19,23,29,31,37,41,43,47,53,59,61,67...
Primes which can be partitioned into a sum of distinct primes in more than one way.
Presumably this consists of all primes except 2, 3 and 11 - see A000586. Prime p is in the
sequence iff A000586(p)>1
5 is a member because 5 = 2+3; 19 because 19 = 3+5+11.
I think that two different sequences have been merged here. One is the simpler "primes
that can be partitioned into a sum of distinct primes", and the other is the same adding
"in more than one way".
5 is not partitioned into a sum of distinct primes in two ways or more, it's just 2+3,
unless you consider 0 to be a prime (this seems to be the rule in A000586, although n|0
for n>0), but considering p+0 to be a prime partition is a bit weird in a primes sequence,
isn't it?
Btw, I don't know either why, in A000586, a(0) = 1... I can't see 0 = p+q with 0<=p<>q>=0,
despite you say 0 is prime or not.
Regards. Jose Brox
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