login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A052294 Pernicious numbers: numbers with a prime number of 1's in their binary expansion. 10
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

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) 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

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 !! (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).

Cf. A262481 (subsequence).

Sequence in context: A242437 A188916 A080943 * A267895 A191916 A254614

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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 30 10:10 EDT 2016. Contains 274307 sequences.