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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

%I #29 Sep 08 2022 08:45:17

%S 6,4,6,14,21,35,10,15,25,35,26,39,65,91,143,22,33,55,77,121,143,38,57,

%T 95,133,209,247,323,34,51,85,119,187,221,289,323,58,87,145,203,319,

%U 377,493,551,667,46,69,115,161,253,299,391,437,529,667,74,111,185,259,407

%N Triangle T(n,k) = prime(k) times the n-th term of (3, 2, 7, 5, 13, 11,...) of a permutation of the primes.

%C 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).

%e Triangle starts:

%e 2* 3;

%e 2* 2, 3* 2;

%e 2* 7, 3* 7, 5* 7;

%e 2* 5, 3* 5, 5* 5, 7* 5;

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

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

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

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

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

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

%e ...

%e =

%e 6;

%e 4,6;

%e 14,21,35;

%e 10,15,25,35;

%e 26,39,65,91,143;

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

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

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

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

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

%e ...

%t 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 *)

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

%o (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

%Y Cf. A105157 (row sums).

%K nonn,less,tabl

%O 1,1

%A _Roger L. Bagula_, Apr 10 2005

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Last modified March 29 04:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)