A375117 Irregular triangle of positive integers, read by rows, the elements of the n-th row being the nonzero remainders, in increasing order, when the Euclidean algorithm is applied to 2^n-1 and n.

1, 1, 1, 3, 1, 3, 1, 1, 7, 1, 2, 7, 1, 3, 1, 3, 1, 1, 2, 3, 1, 7, 1, 15, 1, 9, 1, 5, 15, 7, 1, 3, 1, 3, 6, 9, 15, 1, 6, 1, 2, 3, 1, 2, 25, 1, 2, 13, 15, 1, 3, 1, 1, 31, 1, 2, 5, 7, 1, 3, 1, 17, 9, 27, 1, 1, 2, 3, 1, 3, 4, 7, 5, 10, 15, 1, 21, 1, 1, 14, 15, 1, 3, 13, 16

Offset

2,4

Links

Table of n, a(n) for n=2..86.

Example

The triangle begins:
    1;
    1;
    1, 3;
    1;
    3;
    1;
    1, 7;
    1, 2, 7;
    1, 3;
    1;
    3;
    1;
    3;
    ...
Row(2) is {1}, because 2^2-1 = 4-1 = 3, and 3 divided by 2 leaves a remainder of 1.
Row(4) is {1, 3}, because 2^4-1 = 16-1 = 15, and 15 divided by 4 leaves a remainder of 3, and 4 divided by 3 leaves a remainder of 1.

Prog

(PARI) row(n) = my(x=2^n-1, y=n, ok=1, list=List()); while (ok, my(z=divrem(x, y)); x = y; y = z[2]; if (y==0, ok=0, listput(list, y)); ); listsort(list); Vec(list); \\ Michel Marcus, Jul 31 2024

Crossrefs

Cf. A049816, A014491.

Sequence in context: A128218 A010283 A134699 * A331286 A272880 A003636

Adjacent sequences: A375114 A375115 A375116 * A375118 A375119 A375120

Keyword

nonn,tabf

Author

Mike Jones, Jul 30 2024

Extensions

More terms from Michel Marcus, Jul 31 2024

Status

approved