A371103 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(A371102(n, k)), n,k >= 1.

1, 1, 2, 1, 3, 3, 1, 3, 3, 4, 1, 1, 1, 6, 5, 1, 1, 1, 9, 2, 6, 1, 1, 1, 1, 3, 9, 7, 1, 1, 1, 1, 3, 1, 6, 8, 1, 1, 1, 1, 1, 1, 8, 12, 9, 1, 1, 1, 1, 1, 1, 12, 18, 1, 10, 1, 1, 1, 1, 1, 1, 18, 27, 1, 15, 11, 1, 1, 1, 1, 1, 1, 27, 21, 1, 12, 9, 12, 1, 1, 1, 1, 1, 1, 21, 16, 1, 17, 7, 18, 13, 1, 1, 1, 1, 1, 1, 16, 23, 1, 4, 2, 27, 5, 14

Offset

1,3

Comments

A(n, k) gives the column index of A371102(n, k) in array A257852.

Links

Table of n, a(n) for n=1..105.

Example

Array begins:
n\k| 1  2   3   ...
---+--------------------------------------------------------------------
1  | 1, 2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17,
2  | 1, 3,  3,  6,  2,  9,  6, 12,  1, 15,  9, 18,  5, 21, 12, 24,  4,
3  | 1, 3,  1,  9,  3,  1,  8, 18,  1, 12,  7, 27,  2,  8, 17, 36,  5,
4  | 1, 1,  1,  1,  3,  1, 12, 27,  1, 17,  2, 21,  3, 12,  4, 54,  2,
5  | 1, 1,  1,  1,  1,  1, 18, 21,  1,  4,  2, 16,  3, 18,  5, 81,  3,
6  | 1, 1,  1,  1,  1,  1, 27, 16,  1,  5,  3, 23,  1, 27,  2, 16,  3,
7  | 1, 1,  1,  1,  1,  1, 21, 23,  1,  2,  3, 18,  1, 21,  3, 23,  1,
8  | 1, 1,  1,  1,  1,  1, 16, 18,  1,  3,  1, 26,  1, 16,  3, 18,  1,
9  | 1, 1,  1,  1,  1,  1, 23, 26,  1,  3,  1, 39,  1, 23,  1, 26,  1,
10 | 1, 1,  1,  1,  1,  1, 18, 39,  1,  1,  1, 30,  1, 18,  1, 39,  1,
11 | 1, 1,  1,  1,  1,  1, 26, 30,  1,  1,  1, 44,  1, 26,  1, 30,  1,
12 | 1, 1,  1,  1,  1,  1, 39, 44,  1,  1,  1, 66,  1, 39,  1, 44,  1,
13 | 1, 1,  1,  1,  1,  1, 30, 66,  1,  1,  1, 99,  1, 30,  1, 66,  1,
14 | 1, 1,  1,  1,  1,  1, 44, 99,  1,  1,  1, 75,  1, 44,  1, 99,  1,
15 | 1, 1,  1,  1,  1,  1, 66, 75,  1,  1,  1, 28,  1, 66,  1, 75,  1,
16 | 1, 1,  1,  1,  1,  1, 99, 28,  1,  1,  1, 42,  1, 99,  1, 28,  1,
17 | 1, 1,  1,  1,  1,  1, 75, 42,  1,  1,  1, 63,  1, 75,  1, 42,  1,
18 | 1, 1,  1,  1,  1,  1, 28, 63,  1,  1,  1, 48,  1, 28,  1, 63,  1,
19 | 1, 1,  1,  1,  1,  1, 42, 48,  1,  1,  1, 71,  1, 42,  1, 48,  1,
20 | 1, 1,  1,  1,  1,  1, 63, 71,  1,  1,  1, 54,  1, 63,  1, 71,  1,
21 | 1, 1,  1,  1,  1,  1, 48, 54,  1,  1,  1, 80,  1, 48,  1, 54,  1,

Prog

(PARI)
up_to = 105;
A000265(n) = (n>>valuation(n, 2));
A371092(n) = floor((A000265(1+(3*n))+5)/6);
A371094(n) = { my(m=1+3*n, e=valuation(m, 2)); ((m*(2^e)) + (((4^e)-1)/3)); };
A371102sq(n, k) = if(1==n, 4*k-1, A371094(A371102sq(n-1, k)));
A371103sq(n, k) = A371092(A371102sq(n, k));
A371103list(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] = A371103sq((a-(col-1)), col))); (v); };
v371103 = A371103list(up_to);
A371103(n) = v371103[n];

Crossrefs

Cf. A000027 (row 1), A257852, A371092, A371102.

Cf. also arrays A371097, A371101.

Sequence in context: A098975 A309213 A377433 * A127121 A238703 A185908

Adjacent sequences: A371100 A371101 A371102 * A371104 A371105 A371106

Keyword

nonn,tabl,easy

Author

Antti Karttunen, Apr 21 2024

Status

approved