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Neither a cube nor the sum of a prime and a positive cube.
5

%I #114 Jul 04 2018 05:50:41

%S 2,5,7,9,16,17,22,23,26,28,33,35,36,41,43,47,52,53,57,59,63,65,73,76,

%T 78,82,85,89,92,96,99,103,112,113,118,119,120,122,126,129,133,141,146,

%U 149,151,155,160,163,169,170,179,183,185,188,193,197

%N Neither a cube nor the sum of a prime and a positive cube.

%C Hardy & Littlewood's conjecture that this sequence is finite (Conjecture L, p. 51).

%C Up to 4*10^9 there are 7050 such numbers, the last one being 78526384. - _Giovanni Resta_, Feb 20 2013

%H Giovanni Resta, <a href="/A211167/b211167.txt">Table of n, a(n) for n = 1..7050</a>

%H G. H. Hardy and J. E. Littlewood, <a href="https://dx.doi.org/10.1007/BF02403921">Some problems of 'Partitio numerorum'; III: on the expression of a number as a sum of primes</a>, Acta Mathematica, Vol. 44, pp. 1-70, 1923.

%o (PARI) is(n)=if(ispower(n,3),return(0));for(k=1,n^(1/3),if(isprime(n-k^3), return(0)));1

%Y Cf. A045911.

%K nonn

%O 1,1

%A _Charles R Greathouse IV_, Feb 19 2013