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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

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: A038026 A051860 A155766 * A275115 A085399 A063696

Adjacent sequences:  A153485 A153486 A153487 * A153489 A153490 A153491

KEYWORD

nonn,tabl,easy,less,changed

AUTHOR

Roger L. Bagula, Dec 27 2008

EXTENSIONS

Edited by G. C. Greubel, Mar 02 2021

STATUS

approved

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Last modified March 8 19:52 EST 2021. Contains 341953 sequences. (Running on oeis4.)