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.
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, 13, 6, 3, 508, 252, 188, 40, 26, 11, 8, 3, 1020, 508, 380, 84, 51, 24, 20, 6, 4, 2044, 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
Offset: 1
Examples
Array begins: n\k| 1 2 3 4 5 6 7 8 9 10 11 12 13 14 ---+----------------------------------------------------------------------------- 1 | 0, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 2 | 4, 4, 8, 5, 6, 6, 8, 6, 7, 6, 12, 7, 8, 7, 3 | 12, 12, 20, 10, 13, 11, 20, 11, 16, 13, 28, 11, 14, 12, 4 | 28, 28, 44, 19, 26, 24, 44, 19, 36, 26, 60, 24, 29, 23, 5 | 60, 60, 92, 40, 51, 52, 92, 40, 76, 51, 124, 52, 58, 44, 6 | 124, 124, 188, 84, 104, 108, 188, 84, 156, 104, 252, 108, 115, 84, 7 | 252, 252, 380, 172, 212, 220, 380, 172, 316, 212, 508, 220, 232, 165, 8 | 508, 508, 764, 348, 428, 444, 764, 348, 636, 428, 1020, 444, 468, 326, 9 | 1020, 1020, 1532, 700, 860, 892, 1532, 700, 1276, 860, 2044, 892, 940, 650,
Crossrefs
Programs
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PARI
up_to = 78; A000523(n) = logint(n,2); A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); }; A372282sq(n,k) = if(1==n,2*k-1,A371094(A372282sq(n-1,k))); A372354sq(n,k) = A000523(A372282sq(n,k)); 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); }; v372354 = A372354list(up_to); A372354(n) = v372354[n];