cp's OEIS Frontend

A372354 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.

%I A372354 #8 Apr 30 2024 17:05:34
%S A372354 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 A372354 13,6,3,508,252,188,40,26,11,8,3,1020,508,380,84,51,24,20,6,4,2044,
%U A372354 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 A372354 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 A372354 Array begins:
%e A372354 n\k|    1     2     3    4    5    6     7    8     9   10    11   12   13   14
%e A372354 ---+-----------------------------------------------------------------------------
%e A372354 1  |    0,    1,    2,   2,   3,   3,    3,   3,    4,   4,    4,   4,   4,   4,
%e A372354 2  |    4,    4,    8,   5,   6,   6,    8,   6,    7,   6,   12,   7,   8,   7,
%e A372354 3  |   12,   12,   20,  10,  13,  11,   20,  11,   16,  13,   28,  11,  14,  12,
%e A372354 4  |   28,   28,   44,  19,  26,  24,   44,  19,   36,  26,   60,  24,  29,  23,
%e A372354 5  |   60,   60,   92,  40,  51,  52,   92,  40,   76,  51,  124,  52,  58,  44,
%e A372354 6  |  124,  124,  188,  84, 104, 108,  188,  84,  156, 104,  252, 108, 115,  84,
%e A372354 7  |  252,  252,  380, 172, 212, 220,  380, 172,  316, 212,  508, 220, 232, 165,
%e A372354 8  |  508,  508,  764, 348, 428, 444,  764, 348,  636, 428, 1020, 444, 468, 326,
%e A372354 9  | 1020, 1020, 1532, 700, 860, 892, 1532, 700, 1276, 860, 2044, 892, 940, 650,
%o A372354 (PARI)
%o A372354 up_to = 78;
%o A372354 A000523(n) = logint(n,2);
%o A372354 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372354 A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k)));
%o A372354 A372354sq(n,k) = A000523(A372282sq(n,k));
%o A372354 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 A372354 v372354 = A372354list(up_to);
%o A372354 A372354(n) = v372354[n];
%Y A372354 Cf. A000523, A371094, A372282, A372356 (columnwise first differences), A372357.
%Y A372354 Row 1 is 0 followed by A113473.
%K A372354 nonn,tabl,easy
%O A372354 1,2
%A A372354 _Antti Karttunen_, Apr 30 2024