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A052294
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Pernicious numbers: numbers with a prime number of 1's in their binary expansion.
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19
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3, 5, 6, 7, 9, 10, 11, 12, 13, 14, 17, 18, 19, 20, 21, 22, 24, 25, 26, 28, 31, 33, 34, 35, 36, 37, 38, 40, 41, 42, 44, 47, 48, 49, 50, 52, 55, 56, 59, 61, 62, 65, 66, 67, 68, 69, 70, 72, 73, 74, 76, 79, 80, 81, 82, 84, 87, 88, 91, 93, 94, 96, 97, 98, 100
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OFFSET
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1,1
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COMMENTS
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No power of 2 is pernicious, but 2^n+1 always is.
If a prime p is of the form 2^k -1, then p is included in this sequence. - Leroy Quet, Sep 20 2008
A list of programming codes for pernicious numbers can be found in the Rosetta Code link. - Martin Ettl, May 27 2014
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LINKS
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EXAMPLE
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26 is in the sequence because the binary expansion of 26 is 11010 and 11010 has three 1's and 3 is prime, so the number of 1's in the binary expansion of 26 is prime. - Omar E. Pol, Apr 04 2016
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MAPLE
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filter:= n -> isprime(convert(convert(n, base, 2), `+`)):
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MATHEMATICA
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PROG
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(Haskell)
a052294 n = a052294_list !! (n-1)
a052294_list = filter ((== 1) . a010051 . a000120) [1..]
(Python)
from sympy import isprime
def ok(n): return isprime(bin(n).count("1"))
(Python)
from sympy import isprime
def ok(n): return isprime(n.bit_count())
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CROSSREFS
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KEYWORD
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easy,base,nice,nonn
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AUTHOR
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Jeremy Gow (jeremygo(AT)dai.ed.ac.uk), Feb 08 2000
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STATUS
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approved
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