

A052294


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


9



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

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

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


EXAMPLE

No power of 2 is pernicious, but 2^n+1 always is.


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: A242437 A188916 A080943 * A191916 A254614 A182834
Adjacent sequences: A052291 A052292 A052293 * A052295 A052296 A052297


KEYWORD

easy,nice,nonn,changed


AUTHOR

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


STATUS

approved



