A371097 - OEIS

%I #12 Apr 24 2024 13:58:45

%S 1,1,2,1,2,3,1,3,1,4,1,3,1,5,5,1,1,1,2,4,6,1,1,1,3,5,8,7,1,1,1,3,2,12,

%T 2,8,1,1,1,1,3,18,2,11,9,1,1,1,1,3,27,3,9,7,10,1,1,1,1,1,21,3,7,2,14,

%U 11,1,1,1,1,1,16,1,2,2,21,4,12,1,1,1,1,1,23,1,2,3,8,6,17,13,1,1,1,1,1,18,1,3,3,12,9,4,10,14

%N Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n, k) = A371092(A371095(n, k)), n,k >= 1.

%C A(n, k) gives the column index of A371095(n, k) [or equally, of A371096(n, k)] in array A257852.

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

%F A(n, k) = A371092(A371095(n, k)) = A371092(A371096(n, k)).

%e Array begins:

%e n\k| 1  2  3  ...

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

%e 1  | 1, 2, 3, 4, 5,  6, 7,  8, 9, 10, 11, 12, 13, 14, 15,  16, 17,

%e 2  | 1, 2, 1, 5, 4,  8, 2, 11, 7, 14,  4, 17, 10, 20,  1,  23, 13,

%e 3  | 1, 3, 1, 2, 5, 12, 2,  9, 2, 21,  6,  4, 14, 30,  1,  18, 10,

%e 4  | 1, 3, 1, 3, 2, 18, 3,  7, 2,  8,  9,  5, 21, 45,  1,  26, 14,

%e 5  | 1, 1, 1, 3, 3, 27, 3,  2, 3, 12,  1,  2,  8, 17,  1,  39, 21,

%e 6  | 1, 1, 1, 1, 3, 21, 1,  2, 3, 18,  1,  3, 12,  4,  1,  30,  8,

%e 7  | 1, 1, 1, 1, 1, 16, 1,  3, 1, 27,  1,  3, 18,  5,  1,  44, 12,

%e 8  | 1, 1, 1, 1, 1, 23, 1,  3, 1, 21,  1,  1, 27,  2,  1,  66, 18,

%e 9  | 1, 1, 1, 1, 1, 18, 1,  1, 1, 16,  1,  1, 21,  3,  1,  99, 27,

%e 10 | 1, 1, 1, 1, 1, 26, 1,  1, 1, 23,  1,  1, 16,  3,  1,  75, 21,

%e 11 | 1, 1, 1, 1, 1, 39, 1,  1, 1, 18,  1,  1, 23,  1,  1,  28, 16,

%e 12 | 1, 1, 1, 1, 1, 30, 1,  1, 1, 26,  1,  1, 18,  1,  1,  42, 23,

%e 13 | 1, 1, 1, 1, 1, 44, 1,  1, 1, 39,  1,  1, 26,  1,  1,  63, 18,

%e 14 | 1, 1, 1, 1, 1, 66, 1,  1, 1, 30,  1,  1, 39,  1,  1,  48, 26,

%e 15 | 1, 1, 1, 1, 1, 99, 1,  1, 1, 44,  1,  1, 30,  1,  1,  71, 39,

%e 16 | 1, 1, 1, 1, 1, 75, 1,  1, 1, 66,  1,  1, 44,  1,  1,  54, 30,

%e 17 | 1, 1, 1, 1, 1, 28, 1,  1, 1, 99,  1,  1, 66,  1,  1,  80, 44,

%e 18 | 1, 1, 1, 1, 1, 42, 1,  1, 1, 75,  1,  1, 99,  1,  1, 120, 66,

%e 19 | 1, 1, 1, 1, 1, 63, 1,  1, 1, 28,  1,  1, 75,  1,  1, 180, 99,

%e 20 | 1, 1, 1, 1, 1, 48, 1,  1, 1, 42,  1,  1, 28,  1,  1, 270, 75,

%e 21 | 1, 1, 1, 1, 1, 71, 1,  1, 1, 63,  1,  1, 42,  1,  1, 405, 28,

%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 A371095sq(n,k) = if(1==n,8*k-7,R(A371095sq(n-1,k)));

%o A371097sq(n,k) = A371092(A371095sq(n,k));

%o A371097list(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] = A371097sq((a-(col-1)),col))); (v); };

%o v371097 = A371097list(up_to);

%o A371097(n) = v371097[n];

%Y Cf. A000027 (row 1), A257852, A371092, A371095, A371096.

%Y Cf. also arrays A371101, A371103.

%K nonn,tabl,easy

%O 1,3

%A _Antti Karttunen_, Apr 21 2024