A176041 Triangle read by rows: R(n, k) = 2^(2n - 2) mod prime(2k), 1<=k<=n.

1, 1, 4, 1, 2, 3, 1, 1, 12, 7, 1, 4, 9, 9, 24, 1, 2, 10, 17, 9, 25, 1, 1, 1, 11, 7, 26, 11, 1, 4, 4, 6, 28, 30, 1, 7, 1, 2, 3, 5, 25, 9, 4, 28, 22, 1, 1, 12, 1, 13, 36, 16, 6, 27, 12, 1, 4, 9, 4, 23, 33, 21, 24, 47, 48, 9, 1, 2, 10

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 06 2010

Keywords

• nonn
• tabl

Comments

The leftmost diagonal is all 1s because all even-indexed powers of 2 are congruent to 1 mod 3 (since 3 is the first even-indexed prime).

Examples

			Triangle begins:
1
1, 4
1, 2,  3
1, 1, 12,  7
1, 4,  9,  9, 24
1, 2, 10, 17,  9, 25
For example, R(4, 4) = 7 because 2^(2 * 4 - 2) = 2^6 = 64; the (2 * 4)th prime is 19; and 64 divided by 19 leaves a remainder of 7.
		

Crossrefs

Cf. A000079, A181670.

Programs

Mathematica

ColumnForm[Table[Mod[2^(2n - 2), Prime[2k]], {n, 12}, {k, n}], Center]
Table[PowerMod[2,2n-2,Prime[2k]],{n,15},{k,n}]//Flatten (* Harvey P. Dale, Jul 15 2021 *)