A371095 Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(1, k) = 8*k-7, and A(n+1, k) = R(A(n, k)), n,k >= 1, where Reduced Collatz function R(n) gives the odd part of 3n+1.

1, 1, 9, 1, 7, 17, 1, 11, 13, 25, 1, 17, 5, 19, 33, 1, 13, 1, 29, 25, 41, 1, 5, 1, 11, 19, 31, 49, 1, 1, 1, 17, 29, 47, 37, 57, 1, 1, 1, 13, 11, 71, 7, 43, 65, 1, 1, 1, 5, 17, 107, 11, 65, 49, 73, 1, 1, 1, 1, 13, 161, 17, 49, 37, 55, 81, 1, 1, 1, 1, 5, 121, 13, 37, 7, 83, 61, 89, 1, 1, 1, 1, 1, 91, 5, 7, 11, 125, 23, 67, 97

Offset: 1

Author

Antti Karttunen, Apr 24 2024

Keywords

• nonn
• tabl
• easy

Examples

			Array begins:
n\k|  1   2   3   4   5    6   7   8   9   10  11   12   13   14   15   16
---+------------------------------------------------------------------------
1  |  1,  9, 17, 25, 33,  41, 49, 57, 65,  73, 81,  89,  97, 105, 113, 121,
2  |  1,  7, 13, 19, 25,  31, 37, 43, 49,  55, 61,  67,  73,  79,  85,  91,
3  |  1, 11,  5, 29, 19,  47,  7, 65, 37,  83, 23, 101,  55, 119,   1, 137,
4  |  1, 17,  1, 11, 29,  71, 11, 49,  7, 125, 35,  19,  83, 179,   1, 103,
5  |  1, 13,  1, 17, 11, 107, 17, 37, 11,  47, 53,  29, 125, 269,   1, 155,
6  |  1,  5,  1, 13, 17, 161, 13,  7, 17,  71,  5,  11,  47, 101,   1, 233,
7  |  1,  1,  1,  5, 13, 121,  5, 11, 13, 107,  1,  17,  71,  19,   1, 175,
8  |  1,  1,  1,  1,  5,  91,  1, 17,  5, 161,  1,  13, 107,  29,   1, 263,
9  |  1,  1,  1,  1,  1, 137,  1, 13,  1, 121,  1,   5, 161,  11,   1, 395,
10 |  1,  1,  1,  1,  1, 103,  1,  5,  1,  91,  1,   1, 121,  17,   1, 593,
11 |  1,  1,  1,  1,  1, 155,  1,  1,  1, 137,  1,   1,  91,  13,   1, 445,
12 |  1,  1,  1,  1,  1, 233,  1,  1,  1, 103,  1,   1, 137,   5,   1, 167,
13 |  1,  1,  1,  1,  1, 175,  1,  1,  1, 155,  1,   1, 103,   1,   1, 251,
14 |  1,  1,  1,  1,  1, 263,  1,  1,  1, 233,  1,   1, 155,   1,   1, 377,
15 |  1,  1,  1,  1,  1, 395,  1,  1,  1, 175,  1,   1, 233,   1,   1, 283,
16 |  1,  1,  1,  1,  1, 593,  1,  1,  1, 263,  1,   1, 175,   1,   1, 425,
		

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A017077 (row 1), A016921 (row 2), A075677.

Cf. also A371096, A371097.

Programs

PARI

up_to = 91;
R(n) = { n = 1+3*n; n>>valuation(n, 2); };
A371095sq(n,k) = if(1==n,8*k-7,R(A371095sq(n-1,k)));
A371095list(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] = A371095sq((a-(col-1)),col))); (v); };
v371095 = A371095list(up_to);
A371095(n) = v371095[n];