A324386 - OEIS

%I #11 Feb 28 2019 18:54:14

%S 1,1,2,1,2,2,2,1,4,4,4,2,2,6,6,1,2,4,8,4,4,6,12,2,8,6,10,6,22,10,8,1,

%T 4,4,6,2,8,6,8,4,6,12,14,2,16,10,16,2,8,16,4,6,14,8,24,6,30,18,20,6,

%U 26,18,26,1,6,8,8,4,12,12,6,8,12,14,18,4,20,20,20,4,16,16,8,12,28,16,10,12,22,26,14,12,34,20,22,2,12

%N a(n) = A324383(A006068(n)).

%C This is most likely equal to A276150(A086141(n)), apart from the different offset used in A086141.

%C The same comments about the parity of terms as in A324383 and A324387 apply also here, except here 1's occur at positions given by 2^k - 1.

%H Antti Karttunen, <a href="/A324386/b324386.txt">Table of n, a(n) for n = 0..16383</a>

%H Antti Karttunen, <a href="/A324386/a324386.txt">Data supplement: n, a(n) computed for n = 0..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) = A324383(A006068(n)) = A276150(A322827(A006068(n))).

%F a(A000225(n)) = 1 for all n.

%o (PARI)

%o A006068(n)= { my(s=1, ns); while(1, ns = n >> s; if(0==ns, break()); n = bitxor(n, ns); s <<= 1; ); return (n); } \\ From A006068

%o A276150(n) = { my(s=0,m); forprime(p=2, , if(!n, return(s)); m = n%p; s += m; n = (n-m)/p); };

%o A322827(n) = if(!n,1,my(bits = Vecrev(binary(n)), rl=1, o = List([])); for(i=2,#bits,if(bits[i]==bits[i-1], rl++, listput(o,rl))); listput(o,rl); my(es=Vecrev(Vec(o)), m=1); for(i=1,#es,m *= prime(i)^es[i]); (m));

%o A324383(n) = A276150(A322827(n));

%o A324386(n) = A324383(A006068(n));

%Y Cf. A002110, A006068, A025487, A086141, A276150, A322827, A324342, A324382.

%Y Cf. also A324383, A324387 (permutations of this sequence) and A324380, A324390.

%K nonn

%O 0,3

%A _Antti Karttunen_, Feb 27 2019