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A105160 Triangle T(n,k) = prime(k) times the n-th term of (3, 2, 7, 5, 13, 11,...) of a permutation of the primes. 1
6, 4, 6, 14, 21, 35, 10, 15, 25, 35, 26, 39, 65, 91, 143, 22, 33, 55, 77, 121, 143, 38, 57, 95, 133, 209, 247, 323, 34, 51, 85, 119, 187, 221, 289, 323, 58, 87, 145, 203, 319, 377, 493, 551, 667, 46, 69, 115, 161, 253, 299, 391, 437, 529, 667, 74, 111, 185, 259, 407 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Define the auxiliary sequence 3, 2, 7, 5, 13, 11, 19, 17, 29, 23, 37, 31, 43,.. by b(n)=prime(n-1) if n is even and b(n) = prime(n+1) if n is odd. Then T(n,k) = b(n) *prime(k).

LINKS

Table of n, a(n) for n=1..60.

EXAMPLE

Triangle starts:

2* 3;

2* 2, 3* 2;

2* 7, 3* 7, 5* 7;

2* 5, 3* 5, 5* 5, 7* 5;

2*13, 3*13, 5*13, 7*13,11*13;

2*11, 3*11, 5*11, 7*11,11*11,13*11;

2*19, 3*19, 5*19, 7*19,11*19,13*19,17*19;

2*17, 3*17, 5*17, 7*17,11*17,13*17,17*17,19*17;

2*29, 3*29, 5*29, 7*29,11*29,13*29,17*29,19*29,23*29;

2*23, 3*23, 5*23, 7*23,11*23,13*23,17*23,19*23,23*23,29*23;

...

=

6;

4,6;

14,21,35;

10,15,25,35;

26,39,65,91,143;

22,33,55,77,121,143;

38,57,95,133,209,247,323;

34,51,85,119,187,221,289,323;

58,87,145,203,319,377,493,551,667;

46,69,115,161,253,299,391,437,529,667;

...

MATHEMATICA

T[n_, k_]:=(If[EvenQ[n], (Prime[n-1]), Prime[n+1]]) Prime[k]; Table[T[n, k], {n, 1, 15}, {k, 1, n}]//Flatten (* Vincenzo Librandi, Dec 28 2018 *)

PROG

(PARI) T(n, k) = if (n % 2, prime(n+1), prime(n-1))*prime(k); \\ Michel Marcus, Dec 28 2018

(MAGMA) /* As triangle */ [[(IsOdd(n) select NthPrime(n+1) else NthPrime(n-1))* NthPrime(k): k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Dec 28 2018

CROSSREFS

Cf. A105157 (row sums).

Sequence in context: A216184 A164293 A141796 * A200228 A241297 A021611

Adjacent sequences:  A105157 A105158 A105159 * A105161 A105162 A105163

KEYWORD

nonn,less,tabl

AUTHOR

Roger L. Bagula, Apr 10 2005

STATUS

approved

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Last modified October 18 08:02 EDT 2019. Contains 328146 sequences. (Running on oeis4.)