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# User talk:M. F. Hasler/drafts/SOD-Oct.14

## Contents

## Sequence of the Day : Oct.14, 2010

A057652 Numbers *n* > 2 such that positive values of *n* - 2^{k} are all lucky numbers (*k* > 0).

- { 3, 5, 11, 17, 647, ...}

### 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.

### Comments

#### More terms?

The author who submitted this sequence exactly 10 years ago^{(*)}, asked the question whether there are no more terms.
Since then, this has not been answered. Will the mystery be solved this year ?

- More terms seems rather unlikely, since if you look at
- A039669 Numbers n such that n - 2^k is a prime for all k > 0 with 2^k < n.

- which has the comment:
- Erdos conjectures that these are the only values of n with this property. The conjecture has been verified for n up to 2^77.

- (i.e. 151,115,727,451,828,646,838,272 ≈ 1.5 x 10
^{23}) and consider the fact that Lucky numbers have distribution properties similar to the prime numbers (since they are both the result of some sieving process...) - — Daniel Forgues 00:14, 14 October 2010 (UTC)

Can you suggest a nice little program which efficiently computes the terms of this sequence ?

^{(*)} There is no earlier sequence in OEIS having Oct.14 as recorded birthday, since submissions were not dated before 1996, when the EIS went on-line, and only from 1998 on there has been a substantial number of dated submissions.

#### A057652 definition

A057652 Numbers *n* > 2 such that positive values of *n* - 2^{k} are all lucky numbers (*k* > 0).

I first thought it meant: for some *k* s.t. 1 < 2^{k} < *n*, not for all *k* s.t. 1 < 2^{k} < *n*. I would suggest the definition

A057652 Numbers *n* > 2 such *n* - 2^{k} are all lucky numbers (for all *k* s.t. 1 < 2^{k} < *n*).

— Daniel Forgues 23:49, 13 October 2010 (UTC)

### See also

- A000959: Lucky numbers
- History of the OEIS (on the web site of the OEIS Foundation)

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