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A215151 a(1) = 1; thereafter a(n+1) = 0 if bigomega(n) = bigomega(2^a(n)+n), otherwise a(n+1) = a(n)+1.

%I A215151 #14 Jun 27 2017 19:27:52
%S A215151 1,2,3,0,1,0,1,2,0,0,1,0,1,2,3,4,5,6,7,8,9,0,1,2,3,0,1,2,3,0,1,2,3,4,
%T A215151 5,6,0,1,2,3,4,5,6,0,0,1,2,3,4,0,1,2,3,0,1,0,1,2,0,1,2,3,4,5,0,1,0,1,
%U A215151 0,1,2,3,0,1,2,3,4,0,1,2,3,4,5,6,7,0,0,1,0,1,2,0,1,0,0,1,2,0,0,1,2,3,0,1
%N A215151 a(1) = 1; thereafter a(n+1) = 0 if bigomega(n) = bigomega(2^a(n)+n), otherwise a(n+1) = a(n)+1.
%e A215151 a(2)=2 (=a(1)+1) because A001222(1)=0 < A001222(2^1+1)=A001222(3)=1;
%e A215151 a(3)=3 (=a(2)+1) because A001222(2)=1 < A001222(2^2+2)=A001222(6)=2;
%e A215151 a(4)=0 (=0) because A001222(3)=1 = A001222(2^3+3)=A001222(11)=1;
%e A215151 a(5)=1 (=a(4)+1) because A001222(4)=2 > A001222(2^0+4)=A001222(5)=1;
%e A215151 a(6)=0 (=0) because A001222(5)=1 = A001222(2^1+5)=A001222(7)=1;
%e A215151 a(7)=1 (=a(6)+1) because A001222(6)=2 > A001222(2^0+6)=A001222(7)=1;
%e A215151 a(8)=2 (=a(7)+1) because A001222(7)=1 < A001222(2^1+7)=A001222(9)=2;
%e A215151 a(9)=0 (=0) because A001222(8)=3 = A001222(2^2+8)=A001222(12)=3.
%p A215151 A215151 := proc(n)
%p A215151         option remember;
%p A215151         if n = 1 then
%p A215151                 1;
%p A215151         elif  numtheory[bigomega](n-1) = numtheory[bigomega](2^procname(n-1)+n-1) then
%p A215151                 0 ;
%p A215151         else
%p A215151                 procname(n-1)+1 ;
%p A215151         end if;
%p A215151 end proc: # _R. J. Mathar_, Aug 07 2012
%t A215151 nxt[{n_,a_}]:={n+1,If[PrimeOmega[n]==PrimeOmega[2^a+n],0,a+1]}; Transpose[ NestList[nxt,{1,1},110]][[2]] (* _Harvey P. Dale_, Jun 17 2015 *)
%Y A215151 Cf. A001222, A215020.
%K A215151 nonn,less
%O A215151 1,2
%A A215151 _Gerasimov Sergey_, Aug 04 2012