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A267289
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Primes p such that (2^k)+p+(2^(k+1)) is also prime, where 2^k is the largest power of 2 smaller than p.
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1
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5, 7, 13, 19, 23, 31, 41, 43, 53, 61, 71, 79, 89, 101, 137, 139, 157, 163, 173, 179, 193, 223, 229, 233, 263, 271, 281, 283, 293, 349, 383, 419, 433, 449, 461, 463, 491, 509, 547, 563, 577, 593, 601, 607, 617, 643, 677, 701, 733, 751, 757, 761, 773, 797, 811, 821, 853, 857, 863, 881, 887, 911, 937, 941, 967
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OFFSET
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1,1
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COMMENTS
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LINKS
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EXAMPLE
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p = 5: 4 + 5 + 8 = 17 (is prime).
p = 7: 4 + 7 + 8 = 19 (is prime).
p = 31: 16 + 31 + 32 = 79 (is prime).
p = 43: 32 + 43 + 64 = 139 (is prime).
p = 71: 64 + 71 + 128 = 263 (is prime).
p = 89: 64 + 89 + 128 = 281 (is prime).
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MAPLE
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select(t -> isprime(t) and isprime(t + 3*2^ilog2(t)), [seq(i, i=3..10^4, 2)]); # Robert Israel, Jan 13 2016
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MATHEMATICA
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Select[Prime@ Range@ 165, Function[k, PrimeQ[(2^k) + # + (2^(k + 1))]]@ Floor@ Log2@ # &] (* Michael De Vlieger, Jan 12 2016 *)
lp2Q[p_]:=Module[{k=Floor[Log[2, p]]}, PrimeQ[2^k+p+2^(k+1)]]; Select[ Prime[ Range[200]], lp2Q] (* Harvey P. Dale, Nov 02 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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