cp's OEIS Frontend

A372287 Array read by upward antidiagonals: A(n, k) = A371092(A372283(n, k)), n,k >= 1.

%I A372287 #9 Apr 28 2024 21:23:57
%S A372287 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 A372287 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 A372287 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 A372287 Array read by upward antidiagonals: A(n, k) = A371092(A372283(n, k)), n,k >= 1.
%C A372287 A(n, k) gives the column index of A372282(n, k) [or equally, of A372283(n, k)] in array A257852.
%C A372287 Collatz conjecture is equal to the claim that in each column 1 will eventually appear.
%H A372287 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F A372287 A(n, k) = A371092(A372282(n,k)) = A371092(A372283(n,k)).
%e A372287 Array begins:
%e A372287 n\k| 1  2  3  4  5  6  7  8  9 10 11 12 13  14 15  16 17 18 19  20
%e A372287 ---+---------------------------------------------------------------
%e A372287 1  | 1, 1, 1, 2, 2, 3, 1, 4, 3, 5, 1, 6, 4,  7, 2,  8, 5, 9, 2, 10,
%e A372287 2  | 1, 1, 1, 3, 2, 3, 1, 6, 1, 2, 1, 9, 5,  6, 3, 12, 4, 1, 2, 15,
%e A372287 3  | 1, 1, 1, 3, 3, 1, 1, 9, 1, 3, 1, 1, 2,  8, 3, 18, 5, 1, 3, 12,
%e A372287 4  | 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 12, 1, 27, 2, 1, 3, 17,
%e A372287 5  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 18, 1, 21, 3, 1, 1,  4,
%e A372287 6  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 27, 1, 16, 3, 1, 1,  5,
%e A372287 7  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 21, 1, 23, 1, 1, 1,  2,
%e A372287 8  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 16, 1, 18, 1, 1, 1,  3,
%e A372287 9  | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 23, 1, 26, 1, 1, 1,  3,
%e A372287 10 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 18, 1, 39, 1, 1, 1,  1,
%e A372287 11 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 26, 1, 30, 1, 1, 1,  1,
%e A372287 12 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 39, 1, 44, 1, 1, 1,  1,
%e A372287 13 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 30, 1, 66, 1, 1, 1,  1,
%e A372287 14 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 44, 1, 99, 1, 1, 1,  1,
%e A372287 15 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 66, 1, 75, 1, 1, 1,  1,
%e A372287 16 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 99, 1, 28, 1, 1, 1,  1,
%e A372287 17 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 75, 1, 42, 1, 1, 1,  1,
%e A372287 18 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 28, 1, 63, 1, 1, 1,  1,
%e A372287 19 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 42, 1, 48, 1, 1, 1,  1,
%e A372287 20 | 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 63, 1, 71, 1, 1, 1,  1,
%o A372287 (PARI)
%o A372287 up_to = 105;
%o A372287 A000265(n) = (n>>valuation(n,2));
%o A372287 A371092(n) = floor((A000265(1+(3*n))+5)/6);
%o A372287 R(n) = { n = 1+3*n; n>>valuation(n, 2); };
%o A372287 A372283sq(n,k) = if(1==n,2*k-1,R(A372283sq(n-1,k)));
%o A372287 A372287sq(n,k) = A371092(A372283sq(n,k));
%o A372287 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 A372287 v372287 = A372287list(up_to);
%o A372287 A372287(n) = v372287[n];
%Y A372287 Cf. A257852, A371092, A371094, A372282, A372283, A372288.
%Y A372287 Cf. also A371097 (array giving every fourth column, 1, 5, 9, ...), A371103 (array giving every even numbered column), also array A371101.
%K A372287 nonn,tabl
%O A372287 1,10
%A A372287 _Antti Karttunen_, Apr 28 2024