A153488 Triangle T(n, k) = prime(n)^k - 2^(2*k-3) with T(n, 1) = prime(n), read by rows.

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

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

Sequence in context: A051860 A351494 A155766 * A275115 A085399 A063696

Adjacent sequences: A153485 A153486 A153487 * A153489 A153490 A153491

Keyword

nonn,tabl,easy,less

Author

Roger L. Bagula, Dec 27 2008

Extensions

Edited by G. C. Greubel, Mar 02 2021

Status

approved