OFFSET
1,1
COMMENTS
Row sums are: {2, 10, 145, 2758, 176985, 5228360, 435982109, 17927083398, 1883023193293, 435732491457588, ...}
LINKS
G. C. Greubel, Rows n = 1..50 of the triangle, flattened
FORMULA
T(n, k) = prime(n)^k - 2^(2*k - 3) with T(n, 1) = prime(n).
EXAMPLE
Triangle begins as:
2;
3, 7;
5, 23, 117;
7, 47, 335, 2369;
11, 119, 1323, 14609, 160923;
13, 167, 2189, 28529, 371165, 4826297;
17, 287, 4905, 83489, 1419729, 24137057, 410336625;
19, 359, 6851, 130289, 2475971, 47045369, 893869691, 16983554849;
MAPLE
A153488:= (n, k) -> `if`(k=1, ithprime(n), ithprime(n)^k - 2^(2*k-3));
seq(seq(A153488(n, k), k = 1..n), n = 1..12); # G. C. Greubel, Mar 02 2021
MATHEMATICA
T[n_, k_]:= T[n, k]= If[k==1, Prime[n], Prime[n]^k -2^(2*k-3)];
Table[T[n, k], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Mar 02 2021 *)
PROG
(Sage)
def A153488(n, k): return nth_prime(n)^k - 2^(2*k-3)*(1- kronecker_delta(k, 1))
flatten([[A153488(n, k) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Mar 02 2021
(Magma)
A153488:= func< n, k | k eq 1 select NthPrime(n) else NthPrime(n)^k - 2^(2*k-3) >;
[A153488(n, k): k in [1..n], n in [1..12]]; // G. C. Greubel, Mar 02 2021
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Dec 27 2008
EXTENSIONS
Edited by G. C. Greubel, Mar 02 2021
STATUS
approved