

A100350


Primes p such that p2^k is a prime or semiprime for all k > 0 with 2^k < p.


3




OFFSET

1,1


COMMENTS

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


LINKS

Table of n, a(n) for n=1..8.


EXAMPLE

37 is here because 372, 374, 3716 are semiprimes and 378, 3732 are primes.


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=n2^k; p>0 && (SemiPrimeQ[p]  PrimeQ[p]), k++ ]; If[p<=0, AppendTo[lst, n]], {i, 2, 1000}]; lst


CROSSREFS

Cf. A039669 (n such that n2^k is prime), A100349 (n such that n2^k is prime or semiprime), A100351 (n such that n2^k is semiprime).
Sequence in context: A063911 A087489 A155488 * A084467 A245179 A297177
Adjacent sequences: A100347 A100348 A100349 * A100351 A100352 A100353


KEYWORD

more,nonn


AUTHOR

T. D. Noe, Nov 18 2004


STATUS

approved



