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Numbers that are not the sum of distinct primes with prime subscripts.
5

%I #9 Jul 11 2012 14:56:54

%S 1,2,4,6,7,9,10,12,13,15,18,21,23,24,26,27,29,30,32,35,37,38,40,43,54,

%T 65,68,71,82,85,96

%N Numbers that are not the sum of distinct primes with prime subscripts.

%C Same as numbers <= 96 that are not the sum of distinct primes 3, 5, 11, 17, 31, 41, 59, 67, 83 (= terms of A006450 <= 96), because Dressler and Parker prove that every integer > 96 is a sum of distinct terms of A006450 (primes with prime subscripts).

%H R. E. Dressler and S. T. Parker, <a href="http://dx.doi.org/10.1145/321892.321900">Primes with a prime subscript</a>, J. ACM 22 (1975) 380-381.

%e Prime(Prime(1)) = Prime(2) = 3 and Prime(Prime(2)) = Prime(3) = 5, so 1, 2, and 4 are members, but 3, 5, and 3+5=8 are not.

%Y Cf. A006450, A185723 (complement), A185724, A214296.

%K full,fini,nonn

%O 1,2

%A _Jonathan Sondow_, Jul 10 2012