A202149 Triangle read by rows: T(n, k) = mod(2^k, n), where 1 <= k < n.

0, 2, 1, 2, 0, 0, 2, 4, 3, 1, 2, 4, 2, 4, 2, 2, 4, 1, 2, 4, 1, 2, 4, 0, 0, 0, 0, 0, 2, 4, 8, 7, 5, 1, 2, 4, 2, 4, 8, 6, 2, 4, 8, 6, 2, 2, 4, 8, 5, 10, 9, 7, 3, 6, 1, 2, 4, 8, 4, 8, 4, 8, 4, 8, 4, 8, 2, 4, 8, 3, 6, 12, 11, 9, 5, 10, 7, 1, 2, 4, 8, 2, 4, 8, 2, 4

Offset: 2

Author

Alonso del Arte, Dec 12 2011

Keywords

• nonn
• tabl
• easy

Comments

Rows indexed by odd primes end in 1 (and of course so do rows indexed by base 2 pseudoprimes, A001567). Of those rows, the ones that are permutations of the integers 1 to p - 1 correspond to primes with primitive root 2 (A001122).

Examples

			Triangle starts:
0
2 1
2 0 0
2 4 3 1
2 4 2 4  2
2 4 1 2  4 1
2 4 0 0  0 0 0
2 4 8 7  5 1 2 4
2 4 8 6  2 4 8 6 2
2 4 8 5 10 9 7 3 6 1
2 4 8 4  8 4 8 4 8 4 8
		

Links

• T. D. Noe, Rows n = 2..100, flattened

Crossrefs

Cf. A036117, 2^n mod 11; A036118, 2^n mod 13; A201908, irregular triangle of 2^k mod (2n - 1).

Programs

Mathematica

ColumnForm[Table[PowerMod[2, k, n], {n, 2, 20}, {k, n - 1}], Center]