A178350 Semiprimes with both a prime number of 0's and a prime number of 1's in their binary representations.
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
Examples
a(1)=9 because 9(written in base 10)=1001 where 2=prime number of 0's and 2=prime number of 1's.
Links
- Harvey P. Dale, Table of n, a(n) for n = 1..1000
Programs
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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
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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 *)
Extensions
Corrected (167 removed) by R. J. Mathar, Aug 12 2010