A372287 - OEIS

%I #9 Apr 28 2024 21:23:57

%S 1,1,1,1,1,1,1,1,1,2,1,1,1,3,2,1,1,1,3,2,3,1,1,1,1,3,3,1,1,1,1,1,3,1,

%T 1,4,1,1,1,1,1,1,1,6,3,1,1,1,1,1,1,1,9,1,5,1,1,1,1,1,1,1,1,1,2,1,1,1,

%U 1,1,1,1,1,1,1,3,1,6,1,1,1,1,1,1,1,1,1,3,1,9,4,1,1,1,1,1,1,1,1,1,1,1,1,5,7

%N Array read by upward antidiagonals: A(n, k) = A371092(A372283(n, k)), n,k >= 1.

%C A(n, k) gives the column index of A372282(n, k) [or equally, of A372283(n, k)] in array A257852.

%C Collatz conjecture is equal to the claim that in each column 1 will eventually appear.

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%F A(n, k) = A371092(A372282(n,k)) = A371092(A372283(n,k)).

%e Array begins:

%e n\k| 1  2  3  4  5  6  7  8  9 10 11 12 13  14 15  16 17 18 19  20

%e ---+---------------------------------------------------------------

%e 1  | 1, 1, 1, 2, 2, 3, 1, 4, 3, 5, 1, 6, 4,  7, 2,  8, 5, 9, 2, 10,

%e 2  | 1, 1, 1, 3, 2, 3, 1, 6, 1, 2, 1, 9, 5,  6, 3, 12, 4, 1, 2, 15,

%e 3  | 1, 1, 1, 3, 3, 1, 1, 9, 1, 3, 1, 1, 2,  8, 3, 18, 5, 1, 3, 12,

%e 4  | 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 12, 1, 27, 2, 1, 3, 17,

%e 5  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 18, 1, 21, 3, 1, 1,  4,

%e 6  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 16, 3, 1, 1,  5,

%e 7  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 21, 1, 23, 1, 1, 1,  2,

%e 8  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 18, 1, 1, 1,  3,

%e 9  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 1, 26, 1, 1, 1,  3,

%e 10 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 1, 39, 1, 1, 1,  1,

%e 11 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 26, 1, 30, 1, 1, 1,  1,

%e 12 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 39, 1, 44, 1, 1, 1,  1,

%e 13 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 30, 1, 66, 1, 1, 1,  1,

%e 14 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 44, 1, 99, 1, 1, 1,  1,

%e 15 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 66, 1, 75, 1, 1, 1,  1,

%e 16 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 99, 1, 28, 1, 1, 1,  1,

%e 17 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 75, 1, 42, 1, 1, 1,  1,

%e 18 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 28, 1, 63, 1, 1, 1,  1,

%e 19 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 42, 1, 48, 1, 1, 1,  1,

%e 20 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 63, 1, 71, 1, 1, 1,  1,

%o (PARI)

%o up_to = 105;

%o A000265(n) = (n>>valuation(n,2));

%o A371092(n) = floor((A000265(1+(3*n))+5)/6);

%o R(n) = { n = 1+3*n; n>>valuation(n, 2); };

%o A372283sq(n,k) = if(1==n,2*k-1,R(A372283sq(n-1,k)));

%o A372287sq(n,k) = A371092(A372283sq(n,k));

%o A372287list(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] = A372287sq((a-(col-1)),col))); (v); };

%o v372287 = A372287list(up_to);

%o A372287(n) = v372287[n];

%Y Cf. A257852, A371092, A371094, A372282, A372283, A372288.

%Y Cf. also A371097 (array giving every fourth column, 1, 5, 9, ...), A371103 (array giving every even numbered column), also array A371101.

%K nonn,tabl

%O 1,10

%A _Antti Karttunen_, Apr 28 2024