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%I #5 Apr 30 2024 17:05:23
%S 4,8,3,16,8,6,32,16,12,3,64,32,24,5,3,128,64,48,9,7,3,256,128,96,21,
%T 13,5,5,512,256,192,44,25,13,12,3,1024,512,384,88,53,28,24,5,3,2048,
%U 1024,768,176,108,56,48,8,9,2,4096,2048,1536,352,216,112,96,21,20,7,8,8192,4096,3072,704,432,224,192,44,40,13,16,3
%N Array read by upward antidiagonals: A(n, k) = A372354(1+n,k)-A372354(n,k), n,k >= 1.
%e Array begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%e ---+-----------------------------------------------------------------------------
%e 1 | 4, 3, 6, 3, 3, 3, 5, 3, 3, 2, 8, 3, 4, 3,
%e 2 | 8, 8, 12, 5, 7, 5, 12, 5, 9, 7, 16, 4, 6, 5,
%e 3 | 16, 16, 24, 9, 13, 13, 24, 8, 20, 13, 32, 13, 15, 11,
%e 4 | 32, 32, 48, 21, 25, 28, 48, 21, 40, 25, 64, 28, 29, 21,
%e 5 | 64, 64, 96, 44, 53, 56, 96, 44, 80, 53, 128, 56, 57, 40,
%e 6 | 128, 128, 192, 88, 108, 112, 192, 88, 160, 108, 256, 112, 117, 81,
%e 7 | 256, 256, 384, 176, 216, 224, 384, 176, 320, 216, 512, 224, 236, 161,
%e 8 | 512, 512, 768, 352, 432, 448, 768, 352, 640, 432, 1024, 448, 472, 324,
%e 9 | 1024, 1024, 1536, 704, 864, 896, 1536, 704, 1280, 864, 2048, 896, 944, 647,
%o (PARI)
%o up_to = 78;
%o A000523(n) = logint(n,2);
%o A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
%o A372356sq(n,k) = { my(x=A372282sq(n,k)); (A000523(A371094(x))-A000523(x)); };
%o A372356list(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] = A372356sq((a-(col-1)),col))); (v); };
%o v372356 = A372356list(up_to);
%o A372356(n) = v372356[n];
%Y Columnwise first differences of A372354.
%Y Cf. A000523, A371094, A372282, A372357.
%K nonn,tabl
%O 1,1
%A _Antti Karttunen_, Apr 30 2024
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