

A052294


Pernicious numbers: numbers with a prime number of 1's in their binary expansion.


13



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

1,1


COMMENTS

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
There are A121497(n) nbit members of this sequence.  Charles R Greathouse IV, Mar 22 2013
A list of programming codes for pernicious numbers can be found in the Rosetta Code link.  Martin Ettl, May 27 2014


LINKS

Iain Fox, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe, terms 1001..4000 from Daniel Arribas)
Rosetta Code, Pernicious numbers


EXAMPLE

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


MAPLE

filter:= n > isprime(convert(convert(n, base, 2), `+`)):
select(filter, [$1..1000]); # Robert Israel, Oct 19 2014


MATHEMATICA

Select[Range[6! ], PrimeQ[DigitCount[ #, 2][[1]]]&] (* Vladimir Joseph Stephan Orlovsky, Feb 16 2010 *)


PROG

(Haskell)
a052294 n = a052294_list !! (n1)
a052294_list = filter ((== 1) . a010051 . a000120) [1..]
 Reinhard Zumkeller, Nov 16 2012
(PARI) is(n)=isprime(hammingweight(n)) \\ Charles R Greathouse IV, Mar 22 2013


CROSSREFS

Cf. A000069, A001969, A010051, A000120, A081092 (primes).
Cf. A262481 (subsequence).
Sequence in context: A276278 A277727 A080943 * A267895 A191916 A254614
Adjacent sequences: A052291 A052292 A052293 * A052295 A052296 A052297


KEYWORD

easy,base,nice,nonn


AUTHOR

Jeremy Gow (jeremygo(AT)dai.ed.ac.uk), Feb 08 2000


STATUS

approved



