A100350 Primes p such that p-2^k is a prime or semiprime for all k > 0 with 2^k < p.

7, 11, 13, 19, 23, 37, 41, 73

Offset: 1

Author

T. D. Noe, Nov 18 2004

Keywords

• more
• nonn

Comments

These are the primes in A100349. No others < 10^9; conjecture that this sequence is finite.

Examples

			37 is here because 37-2, 37-4, 37-16 are semiprimes and 37-8, 37-32 are primes.
		

Crossrefs

Cf. A039669 (n such that n-2^k is prime), A100349 (n such that n-2^k is prime or semiprime), A100351 (n such that n-2^k is semiprime).

Programs

Mathematica

SemiPrimeQ[n_Integer] := If[Abs[n]<2, False, (2==Plus@@Transpose[FactorInteger[Abs[n]]][[2]])]; lst={}; Do[k=1; While[n=Prime[i]; p=n-2^k; p>0 && (SemiPrimeQ[p] || PrimeQ[p]), k++ ]; If[p<=0, AppendTo[lst, n]], {i, 2, 1000}]; lst