A283472 - OEIS

%I #12 Mar 19 2017 01:09:04

%S 0,0,1,1,0,2,2,2,2,3,0,0,4,4,4,4,4,5,4,5,5,6,0,0,0,0,0,8,8,8,8,8,8,9,

%T 8,9,8,8,8,8,10,10,10,11,11,12,12,12,13,0,0,0,0,0,0,0,0,0,16,16,16,16,

%U 16,16,16,17,16,17,16,17,17,16,18,18,16,16,16,17,18,18,16,16,16,17,17,17,18,20,20,20,21,22,22,24,24,24,24

%N a(n) = A004001(A004001(n-1)) AND A004001(n-A004001(n-1)), a(1) = a(2) = 0.

%H Antti Karttunen, <a href="/A283472/b283472.txt">Table of n, a(n) for n = 1..16384</a>

%F a(1) = a(2) = 0; for n > 2, a(n) = A004001(A004001(n-1)) AND A004001(A080677(n-1)), where AND is bitwise-and (A004198).

%F Other identities. For all n >= 1:

%F a(n) = A283469(n) - A283470(n).

%F A004001(n) = A283469(n) + a(n) = A283470(n) + 2*a(n).

%t a[n_] := a[n] = If[n <= 2, 1, a[a[n - 1]] + a[n - a[n - 1]]]; Table[BitAnd[a[#], a[n - #]] &@ a[n - 1] - Boole[n <= 2], {n, 97}] (* _Michael De Vlieger_, Mar 18 2017, after _Robert G. Wilson v_ at A004001 *)

%o (Scheme) (define (A283472 n) (if (<= n 2) 0 (A004198bi (A004001 (A004001 (- n 1))) (A004001 (- n (A004001 (- n 1)))))))

%o ;; A004198bi implements bitwise-AND (see A004198). Code for A004001 given under that entry.

%Y Cf. A004001, A004198, A283469, A283470, A283473 (positions of zeros).

%K nonn

%O 1,6

%A _Antti Karttunen_, Mar 18 2017