A057652 Numbers n such that n-2^k is a lucky number for all k such that 1 < 2^k < n.

1, 2, 3, 5, 11, 17, 647

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

Table of n, a(n) for n=1..7.

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

Cf. A000959, A039669.

Sequence in context: A359630 A244914 A227126 * A025067 A024371 A344963

Adjacent sequences: A057649 A057650 A057651 * A057653 A057654 A057655

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