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.

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

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 * A353773 A200228 A309710

Adjacent sequences: A105157 A105158 A105159 * A105161 A105162 A105163

Keyword

nonn,less,tabl

Author

Roger L. Bagula, Apr 10 2005

Status

approved