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A052294 Pernicious numbers: numbers with a prime number of 1's in their binary expansion. 8
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 (list; graph; refs; listen; history; text; internal format)
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) n-bit 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 !! (n-1)

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).

Sequence in context: A242437 A188916 A080943 * A191916 A182834 A116883

Adjacent sequences:  A052291 A052292 A052293 * A052295 A052296 A052297

KEYWORD

easy,nice,nonn

AUTHOR

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

STATUS

approved

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Last modified December 22 21:10 EST 2014. Contains 252372 sequences.