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A372359 Array read by upward antidiagonals: A(n, k) = A372358(A372282(n, k)), n,k >= 1.

%I A372359 #7 May 01 2024 08:58:16
%S A372359 0,0,0,0,0,0,0,0,0,2,0,0,0,24,4,0,0,0,256,32,6,0,0,0,0,6144,16,0,0,0,
%T A372359 0,0,16777216,0,0,2,0,0,0,0,0,0,0,8,4,0,0,0,0,0,0,0,1408,0,6,0,0,0,0,
%U A372359 0,0,0,0,0,32,0,0,0,0,0,0,0,0,0,0,6144,0,2,0,0,0,0,0,0,0,0,0,16777216,0,88,12
%N A372359 Array read by upward antidiagonals: A(n, k) = A372358(A372282(n, k)), n,k >= 1.
%C A372359 Zeros occur in the same locations as where they occur in A372353 and where 1's occur in array A372287.
%F A372359 A(n, k) = A372282(n,k) XOR A086893(1+A372354(n, k)), where XOR is bitwise-xor, A003987.
%e A372359 Array begins:
%e A372359 n\k| 1  2  3    4     5   6  7     8  9    10 11  12         13             14
%e A372359 ---+----------------------------------------------------------------------------
%e A372359 1  | 0, 0, 0,   2,    4,  6, 0,    2, 4,    6, 0,  2,        12,            14,
%e A372359 2  | 0, 0, 0,  24,   32, 16, 0,    8, 0,   32, 0, 88,        96,           112,
%e A372359 3  | 0, 0, 0, 256, 6144,  0, 0, 1408, 0, 6144, 0,  0,      8192,          2560,
%e A372359 4  | 0, 0, 0,   0, 2^24,  0, 0,    0, 0, 2^24, 0,  0, 402653184,       6815744,
%e A372359 5  | 0, 0, 0,   0,    0,  0, 0,    0, 0,    0, 0,  0,      2^56, 4947802324992,
%e A372359 6  | 0, 0, 0,   0,    0,  0, 0,    0, 0,    0, 0,  0,         0,     31 * 2^79,
%e A372359 where 2^56 = 72057594037927936 and 31 * 2^79 = 18738350204026752207945728.
%o A372359 (PARI)
%o A372359 up_to = 91;
%o A372359 A000523(n) = logint(n,2);
%o A372359 A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3); \\ From A086893
%o A372359 A372358(n) = bitxor(A086893(1+A000523(n)),n);
%o A372359 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372359 A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
%o A372359 A372359sq(n,k) = A372358(A372282sq(n,k));
%o A372359 A372359list(up_to) = { my(v = vector(up_to), i=0); for(a=1,oo, for(col=1,a, i++; if(i > up_to, return(v)); v[i] = A372359sq((a-(col-1)),col))); (v); };
%o A372359 v372359 = A372359list(up_to);
%o A372359 A372359(n) = v372359[n];
%Y A372359 Cf. A003987, A086893, A371094, A372282, A372287, A372354, A372358, A372360 (binary weights).
%Y A372359 Cf. also A372353.
%K A372359 nonn,tabl
%O A372359 1,10
%A A372359 _Antti Karttunen_, May 01 2024