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A178350
Semiprimes with both a prime number of 0's and a prime number of 1's in their binary representations.
3
9, 10, 21, 22, 25, 26, 35, 38, 49, 65, 87, 91, 93, 94, 115, 118, 121, 122, 133, 134, 143, 145, 146, 155, 158, 161, 185, 194, 203, 205, 206, 213, 214, 217, 218, 319, 381, 382, 415, 445, 446, 471, 478, 493, 501, 502, 505, 515, 517, 527, 529, 535, 542, 545, 551
OFFSET
1,1
LINKS
EXAMPLE
a(1)=9 because 9(written in base 10)=1001 where 2=prime number of 0's and 2=prime number of 1's.
MAPLE
A000120 := proc(n) add(d, d=convert(n, base, 2)) ; end proc:
A080791 := proc(n) dgs :=convert(n, base, 2) ; nops(dgs)-A000120(n) ; end proc:
for n from 1 to 300 do spr :=A001358(n) ; if isprime( A080791(spr) ) and isprime(A000120(spr)) then printf("%d, ", spr) ; end if; end do: # R. J. Mathar, Aug 12 2010
MATHEMATICA
Select[Range[600], PrimeOmega[#]==2&&AllTrue[{DigitCount[ #, 2, 0], DigitCount[ #, 2, 1]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, May 25 2016 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
EXTENSIONS
Corrected (167 removed) by R. J. Mathar, Aug 12 2010
STATUS
approved