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%I #8 Apr 30 2024 17:05:34
%S 0,4,1,12,4,2,28,12,8,2,60,28,20,5,3,124,60,44,10,6,3,252,124,92,19,
%T 13,6,3,508,252,188,40,26,11,8,3,1020,508,380,84,51,24,20,6,4,2044,
%U 1020,764,172,104,52,44,11,7,4,4092,2044,1532,348,212,108,92,19,16,6,4,8188,4092,3068,700,428,220,188,40,36,13,12,4
%N Array read by upward antidiagonals: A(n, k) = A000523(A372282(n, k)), n,k >= 1, where A000523(x) is one less than the number of bits in the binary expansion of x.
%e Array begins:
%e n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14
%e ---+-----------------------------------------------------------------------------
%e 1 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4,
%e 2 | 4, 4, 8, 5, 6, 6, 8, 6, 7, 6, 12, 7, 8, 7,
%e 3 | 12, 12, 20, 10, 13, 11, 20, 11, 16, 13, 28, 11, 14, 12,
%e 4 | 28, 28, 44, 19, 26, 24, 44, 19, 36, 26, 60, 24, 29, 23,
%e 5 | 60, 60, 92, 40, 51, 52, 92, 40, 76, 51, 124, 52, 58, 44,
%e 6 | 124, 124, 188, 84, 104, 108, 188, 84, 156, 104, 252, 108, 115, 84,
%e 7 | 252, 252, 380, 172, 212, 220, 380, 172, 316, 212, 508, 220, 232, 165,
%e 8 | 508, 508, 764, 348, 428, 444, 764, 348, 636, 428, 1020, 444, 468, 326,
%e 9 | 1020, 1020, 1532, 700, 860, 892, 1532, 700, 1276, 860, 2044, 892, 940, 650,
%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 A372354sq(n,k) = A000523(A372282sq(n,k));
%o A372354list(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] = A372354sq((a-(col-1)),col))); (v); };
%o v372354 = A372354list(up_to);
%o A372354(n) = v372354[n];
%Y Cf. A000523, A371094, A372282, A372356 (columnwise first differences), A372357.
%Y Row 1 is 0 followed by A113473.
%K nonn,tabl,easy
%O 1,2
%A _Antti Karttunen_, Apr 30 2024
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