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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 Erdős 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<n || break; setsearch(v, n-2^k) || next(2)); print1(n", ")) } /* M. F. Hasler, Oct 15 2010 */
CROSSREFS
Sequence in context: A359630 A244914 A227126 * A025067 A024371 A344963
KEYWORD
nonn,hard,more
AUTHOR
Naohiro Nomoto, Oct 14 2000
EXTENSIONS
Added initial terms {1, 2}, reworded definition following a suggestion from D. Forgues. - M. F. Hasler, Oct 15 2010
STATUS
approved

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Last modified March 19 06:56 EDT 2024. Contains 370953 sequences. (Running on oeis4.)