A138001 - OEIS

%I #6 Jun 14 2017 01:02:29

%S 1,4,6,8,15,17,19,22,24,25,26,27,28,30,33,35,37,44,46,48,51,54,57,59,

%T 61,68,70,72,75,77,78,79,80,81,83,86,88,90,97,99,101,104,106,108,111,

%U 113,115,122,124,126,129,131,132,133,134,135,137,140,142,144,151,153,155

%N Numbers not representable as sum of elements of A138000.

%C Let R(0)={0} and for n>0, R(n) = R(n-1) union A138000(n)+R(n-1) be the numbers which can be written as sum of some subset of {A138000(1),...,A138000(n)}. A138001 is then the complement of R=union( R(n), n>0) in N.

%F A138001 = N \ { A138000(k[1])+...+ A138000(k[m]) ; m>=0, 0<k[1]<...<k[m] }.

%e A138000=(2,3,7,11,...) and increasing, thus 1,4,6,8,... cannot be written as sum of elements of A138000. To get the numbers which have to be omitted, construct the sets R(1),R(2),... as defined in the comment.

%o (PARI) s=p=q=1; for( n=1,9, while( bitand( s, s>>p=nextprime(p+1)),); s+=s<<p; until( q++>p, bittest( s,q ) || print1( q",")))

%Y Cf. A138000, A064934, A003158.

%K nonn

%O 1,2

%A _M. F. Hasler_, Apr 09 2008