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A100350
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Primes p such that p-2^k is a prime or semiprime for all k > 0 with 2^k < p.
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3
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OFFSET
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1,1
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COMMENTS
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These are the primes in A100349. No others < 10^9; conjecture that this sequence is finite.
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LINKS
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EXAMPLE
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37 is here because 37-2, 37-4, 37-16 are semiprimes and 37-8, 37-32 are primes.
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MATHEMATICA
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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
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CROSSREFS
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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).
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KEYWORD
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more,nonn
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AUTHOR
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STATUS
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approved
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