1,1

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

P. Erdos, On integers of the form 2^k + p and some related questions, Summa Bras. Math., 2 (1950), 113-123.

R. K. Guy, Unsolved Problems in Number Theory, A19.

D. S. Mitrinovic et al., Handbook of Number Theory, Kluwer, p. 306.

D. Wells, Curious and interesting numbers, Penguin Books, p. 118.

45 is here because 43, 41, 37, 29, and 13 are primes.

lst={}; Do[k=1; While[p=n-2^k; p>0 && PrimeQ[p], k++ ]; If[p<=0, AppendTo[lst, n]], {n, 3, 1000}]; lst (T. D. Noe)

Cf. A067526 (n such that n-2^k is prime or 1), A067527 (n such that n-3^k is prime), A067528 (n such that n-4^k is prime or 1), A067529 (n such that n-5^k is prime), A100348 (n such that n-4^k is prime), A100349 (n such that n-2^k is prime or semiprime), A100350 (primes p such that p-2^k is prime or semiprime), A100351 (n such that n-2^k is semiprime).

Sequence in context: A137053 A049832 A092309 this_sequence A109622 A124286 A027419

Adjacent sequences: A039666 A039667 A039668 this_sequence A039670 A039671 A039672

nonn

Felice Russo (felice.russo(AT)katamail.com)

Additional comments from T. D. Noe (noe(AT)sspectra.com), Sep 15 2002