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A153271 Triangle T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 3, read by rows. 3
5, 5, 30, 5, 35, 315, 5, 40, 440, 6160, 5, 45, 585, 9945, 208845, 5, 50, 750, 15000, 375000, 11250000, 5, 55, 935, 21505, 623645, 21827575, 894930575, 5, 60, 1140, 29640, 978120, 39124800, 1838865600, 99298742400, 5, 65, 1365, 39585, 1464645, 65909025, 3493178325, 213083877825, 14702787569925 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are {5, 35, 355, 6645, 219425, 11640805, 917404295, 101177741765, 14919432040765, 2839006665525525, 677815000136926955, ...}.

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

T(n, k) = Product_{j=0..k} (j*n + prime(m)), with T(n, 0) = prime(m) and m = 3.

EXAMPLE

Triangle begins as:

  5;

  5, 30;

  5, 35, 315;

  5, 40, 440,  6160;

  5, 45, 585,  9945, 208845;

  5, 50, 750, 15000, 375000, 11250000;

  5, 55, 935, 21505, 623645, 21827575, 894930575;

MAPLE

m:=3; seq(seq(`if`(k=0, ithprime(m), mul(j*n + ithprime(m), j=0..k)), k=0..n), n=0..10); # G. C. Greubel, Dec 03 2019

MATHEMATICA

T[n_, k_, m_]:= If[k==0, Prime[m], Product[j*n + Prime[m], {j, 0, k}]];

Table[T[n, k, 3], {n, 0, 10}, {k, 0, n}]//Flatten

PROG

(PARI) T(n, k) = my(m=3); if(k==0, prime(m), prod(j=0, k, j*n + prime(m)) ); \\ G. C. Greubel, Dec 03 2019

(MAGMA) m:=3;

function T(n, k)

  if k eq 0 then return NthPrime(m);

  else return (&*[j*n + NthPrime(m): j in [0..k]]);

  end if; return T; end function;

[T(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 03 2019

(Sage)

def T(n, k):

    m=3

    if (k==0): return nth_prime(m)

    else: return product(j*n + nth_prime(m) for j in (0..k))

[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 03 2019

CROSSREFS

Cf. A153271 (m=2), this sequence (m=3), A153272 (m=4).

Sequences related to m values:

m=2: A001147, A001710, A008545, A032031, A047056, A144739, A144758.

m=3: A001720, A007696, A008543, A034000, A051577, A052562, A147585, A147625, A147629.

Sequence in context: A284140 A284182 A020551 * A261569 A117858 A014434

Adjacent sequences:  A153268 A153269 A153270 * A153272 A153273 A153274

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Dec 22 2008

EXTENSIONS

Edited by G. C. Greubel, Dec 03 2019

STATUS

approved

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Last modified April 11 21:23 EDT 2021. Contains 342888 sequences. (Running on oeis4.)