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%I #13 Jun 13 2017 02:19:37
%S 1,2,3,5,11,17,647
%N Numbers n such that n-2^k is a lucky number for all k such that 1 < 2^k < n.
%C Perhaps there are no more terms?
%C Lucky numbers have asymptotic properties very similar to prime numbers, so one can conjecture finiteness of this sequence in the same way as Erdős did for A039669, and this should generalize to any sequence created using a similar sieve. - _M. F. Hasler_, Oct 15 2010
%e 647 is in this sequence since 647-2, 647-4, 647-8, 647-16, 647-32, 647-64, 647-128, 647-256, 647-512 are all members of the sequence A000959 of lucky numbers. - _M. F. Hasler_, Oct 15 2010
%o (PARI) A057652(Nmax) = { my(v=vector(Nmax\2,i,2*i-1)); for(i=2,#v,v[i]>#v && break; v=vecextract(v,2^#v-1-sum(k=1,#v\v[i],2^(v[i]*k))>>1)); v=Set(v); for(n=1,Nmax, for(k=1,Nmax, 2^k<n || break; setsearch(v,n-2^k) || next(2)); print1(n",")) } /* _M. F. Hasler_, Oct 15 2010 */
%Y Cf. A000959, A039669.
%K nonn,hard,more
%O 1,2
%A _Naohiro Nomoto_, Oct 14 2000
%E Added initial terms {1, 2}, reworded definition following a suggestion from D. Forgues. - _M. F. Hasler_, Oct 15 2010
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