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 A057652 Numbers n such that n-2^k is a lucky number for all k such that 1 < 2^k < n. 1
 1, 2, 3, 5, 11, 17, 647 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Perhaps there are no more terms? Lucky numbers have asymptotic properties very similar to prime numbers, so one can conjecture finiteness of this sequence in the same way as ErdÅ‘s did for A039669, and this should generalize to any sequence created using a similar sieve. - M. F. Hasler, Oct 15 2010 LINKS EXAMPLE 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 PROG (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

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Last modified August 10 13:12 EDT 2022. Contains 356039 sequences. (Running on oeis4.)