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

Author

Naohiro Nomoto, Oct 14 2000

Keywords

• nonn
• hard
• more

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

Examples

			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
		

Crossrefs

Cf. A000959, A039669.

Programs

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^kM. F. Hasler, Oct 15 2010 */

Extensions

Added initial terms {1, 2}, reworded definition following a suggestion from D. Forgues. - M. F. Hasler, Oct 15 2010