A177226 Triangle read by rows: T(n, k) = 2^(prime(n) - prime(k)) mod prime(n), 1 <= k <= n.

1, 2, 1, 3, 4, 1, 4, 2, 4, 1, 6, 3, 9, 5, 1, 7, 10, 9, 12, 4, 1, 9, 13, 16, 4, 13, 16, 1, 10, 5, 6, 11, 9, 7, 4, 1, 12, 6, 13, 9, 2, 12, 18, 16, 1, 15, 22, 20, 5, 13, 25, 7, 9, 6, 1, 16, 8, 2, 16, 1, 8, 16, 4, 8, 4, 1, 19, 28, 7, 11, 3, 10, 33, 36, 30, 34, 27, 1, 21, 31, 18, 25, 40, 10, 16, 4, 31, 37, 40, 16, 1

Offset: 1

Author

Juri-Stepan Gerasimov, Dec 10 2010

Keywords

• nonn
• tabl

Examples

			Triangle begins:
   1;
   2,  1;
   3,  4,  1;
   4,  2,  4,  1;
   6,  3,  9,  5,  1;
   7, 10,  9, 12,  4,  1;
   9, 13, 16,  4, 13, 16,  1;
  10,  5,  6, 11,  9,  7,  4,  1;
  12,  6, 13,  9,  2, 12, 18, 16,  1;
		

Links

• G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Crossrefs

Cf. A000079, A111333, A173655, A174497, A174947, A174996, A292411.

Programs

Magma

A177226:= func< n,k | Modexp(2, NthPrime(n) - NthPrime(k), NthPrime(n)) >;
[A177226(n,k): k in [1..n], n in [1..12]]; // G. C. Greubel, Apr 09 2024

Mathematica

Flatten[Table[PowerMod[2,Prime[n]-Prime[k],Prime[n]],{n,20},{k,n}]] (* Harvey P. Dale, May 10 2014 *)

SageMath

def A177226(n,k): return pow(2, nth_prime(n) - nth_prime(k), nth_prime(n))
flatten([[A177226(n,k) for k in range(1,n+1)] for n in range(1,13)]) # G. C. Greubel, Apr 09 2024

Formula

From G. C. Greubel, Apr 09 2024: (Start)

T(n, 1) = A111333(n).

T(n, 2) = A292411(n). (End)

Extensions

Corrected by D. S. McNeil, Dec 10 2010