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A091932
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Primes that remain prime when their leading digit in binary representation is replaced by 0.
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8
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7, 11, 13, 19, 23, 29, 37, 43, 61, 67, 71, 83, 101, 107, 131, 139, 151, 157, 181, 199, 211, 229, 241, 263, 269, 293, 317, 353, 359, 383, 419, 449, 467, 479, 523, 541, 571, 601, 613, 619, 643, 661, 691, 709, 739, 751, 769, 823, 829, 859, 991, 1021, 1031, 1061
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OFFSET
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1,1
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COMMENTS
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Primes p such that p - 2^floor(log_2(p)) is prime - T. D. Noe, Apr 08 2011
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LINKS
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FORMULA
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EXAMPLE
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A000040(12)=37 --> '100101' --> '[1]00101' --> '[0]00101' --> '101' --> 5, therefore 37 is a term.
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MATHEMATICA
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Select[Prime[Range[100]], PrimeQ[# - 2^Floor[Log[2, #]]] &] (* T. D. Noe, Apr 08 2011 *)
Select[Prime[Range[200]], PrimeQ[FromDigits[Rest[ IntegerDigits[ #, 2]], 2]]&] (* Harvey P. Dale, Apr 08 2016 *)
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PROG
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(Python)
from sympy import isprime, primerange
def ok(p): return isprime((1 << (p.bit_length()-1)) ^ p)
def aupto(lim): return [p for p in primerange(1, lim+1) if ok(p)]
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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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