A191401 - OEIS

%I #9 Feb 19 2019 23:35:19

%S 2,9,10,42,44,50,52,135,150,156,184,198,204,210,225,228,232,675,684,

%T 696,728,744,752,920,944,968,976,2484,2544,2646,2673,2744,2772,2835,

%U 2904,2928,2992,3132,3150,3192

%N k-almost primes which are digitally balanced in base 2 and have 2k digits in base 2, for some k >= 1.

%C The sequence contains all terms j of A031443 where A001222(j) = A070939(j)/2.

%e 10=A031443(3) is in the sequence because it has 2 ones and 2 zeros in binary, and is a semiprime (A001358).

%e 50=A031443(12) is in the sequence because it has 3 ones and 3 zeros in binary and is a 3-almost prime (A014612).

%p isA031443 := proc(n) local d2 ; d2 := nops(convert(n,base,2)) ; return( 2*wt(n) = d2 ) ; end proc ;

%p isA191401 := proc(n) local k ; if isA031443(n) then k := nops(convert(n,base,2))/2 ; return( numtheory[bigomega](n) = k ) ; else false; end if; end proc:

%p for n from 1 to 3200 do if isA191401(n) then printf("%d,",n) ; end if; end do: # _R. J. Mathar_, Jun 08 2011

%Y Cf. A031443.

%K nonn,base,less

%O 1,1

%A _Juri-Stepan Gerasimov_, Jun 01 2011

%E Corrected by _R. J. Mathar_, Jun 08 2011