A100349 Numbers n such that n-2^k is a prime or semiprime for all k > 0 with 2^k < n.

4, 6, 7, 8, 11, 13, 15, 19, 21, 23, 25, 27, 37, 39, 41, 45, 51, 55, 57, 63, 69, 73, 75, 81, 87, 93, 99, 105, 111, 117, 123, 135, 147, 153, 159, 165, 171, 195, 201, 213, 219, 225, 231, 237, 243, 255, 267, 273, 285, 297, 315, 321, 363, 369, 399, 405, 411, 423, 435, 447

Offset: 1

Author

T. D. Noe, Nov 18 2004

Keywords

• nonn

Comments

Is the sequence finite? If so, then A039669 is finite.

Examples

			27 is here because 27-2 is a semiprime and 27-4, 27-8 and 27-16 are primes.
		

Links

• T. D. Noe, Table of n < 2^31

Crossrefs

Cf. A039669 (n such that n-2^k is prime), A100350 (primes p such that p-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[p=n-2^k; p>0 && (SemiPrimeQ[p] || PrimeQ[p]), k++ ]; If[p<=0, AppendTo[lst, n]], {n, 3, 1000}]; lst