|
|
A153488
|
|
Triangle T(n, k) = prime(n)^k - 2^(2*k-3) with T(n, 1) = prime(n), read by rows.
|
|
1
|
|
|
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, 23, 527, 12159, 279809, 6436215, 148035377, 3404823399, 78310977089, 1801152628695
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
Row sums are: {2, 10, 145, 2758, 176985, 5228360, 435982109, 17927083398, 1883023193293, 435732491457588, ...}
|
|
LINKS
|
|
|
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));
|
|
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))
(Magma)
A153488:= func< n, k | k eq 1 select NthPrime(n) else NthPrime(n)^k - 2^(2*k-3) >;
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|