A327856 - OEIS

%I #7 Sep 28 2019 22:24:36

%S 1,1,2,1,1,3,1,2,1,4,1,1,3,1,5,1,2,3,2,3,6,1,1,1,1,1,1,7,1,2,1,4,1,2,

%T 1,8,1,1,3,1,3,3,7,1,9,1,2,3,2,5,6,1,2,3,10,1,1,1,1,1,1,1,1,1,1,11,1,

%U 2,3,4,3,6,1,4,3,6,1,12,1,1,1,1,1,1,1,1,1,1,1,1,13,1,2,1,2,1,2,7,2,7,2,1,2,1,14

%N The upper left triangular section of square array A091255, read by rows.

%H Antti Karttunen, <a href="/A327856/b327856.txt">Table of n, a(n) for n = 1..10440; the first 144 rows of triangular table</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>

%F A(n,k) = A091255(n,k), with k in range 1 .. n.

%F a(A000217(n)) = n.

%e The triangular table starts as:

%e   1,

%e   1, 2,

%e   1, 1, 3,

%e   1, 2, 1, 4,

%e   1, 1, 3, 1, 5,

%e   1, 2, 3, 2, 3, 6,

%e   1, 1, 1, 1, 1, 1, 7,

%e   1, 2, 1, 4, 1, 2, 1, 8,

%e   1, 1, 3, 1, 3, 3, 7, 1, 9,

%e   1, 2, 3, 2, 5, 6, 1, 2, 3, 10,

%e   ...

%o (PARI)

%o up_to = 105;

%o A091255sq(a,b) = fromdigits(Vec(lift(gcd(Pol(binary(a))*Mod(1, 2),Pol(binary(b))*Mod(1, 2)))),2);

%o A327856list(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] = A091255sq(a,col))); (v); };

%o v327856 = A327856list(up_to);

%o A327856(n) = v327856[n];

%Y Cf. A000217, A091255.

%K nonn,tabl

%O 1,3

%A _Antti Karttunen_, Sep 28 2019