A382835 Array read by ascending antidiagonals: A(n,k) = (6*n + 1)*(12*n + 1)*Product_{i=0..k-2} (9*2^i*n + 1) with k >= 2.
1, 91, 1, 325, 1729, 1, 703, 12025, 63973, 1, 1225, 38665, 877825, 4670029, 1, 1891, 89425, 4214485, 127284625, 677154205, 1, 2701, 172081, 12966625, 914543245, 36785256625, 195697565245, 1, 3655, 294409, 31146661, 3747354625, 395997225085, 21225093072625, 112917495146365, 1
Offset: 0
Examples
The array begins as:
1, 1, 1, 1, 1, ...
91, 1729, 63973, 4670029, 677154205, ...
325, 12025, 877825, 127284625, 36785256625, ...
703, 38665, 4214485, 914543245, 395997225085, ...
1225, 89425, 12966625, 3747354625, 2162223618625, ...
1891, 172081, 31146661, 11243944621, 8106884071741, ...
2701, 294409, 63886753, 27662964049, 23928463902385, ...
...
References
- Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 101.
Programs
-
Mathematica
A[n_,k_]:=(6n+1)(12n+1)Product[9*2^i*n+1,{i,k-2}];Table[A[n-k,k],{n,0,9},{k,2,n}]//Flatten
Comments