OFFSET
1,1
COMMENTS
First column: A016957, second column: A017341, third column: 2*A017029, fourth column: A082286. - Vincenzo Librandi, Nov 21 2012
Conjecture: Let p = prime number. If 2^p belongs to the sequence, then 2^p-1 is not a Mersenne prime. - Vincenzo Librandi, Dec 12 2012
Conjecture is true because if T(n, k) = 2^p with p prime, then 2^p-1 = 4*n*k + 2*n + 2*k + 1 = (2*n+1)*(2*k+1) hence 2^p-1 is not prime. - Michel Marcus, May 31 2015
It appears that T(m,p) = 2^p for Lucasian primes (A002515) greater than 3. For instance: T(44, 11) = 2^11, T(89240, 23) = 2^23. - Michel Marcus, May 28 2015
For n > 1, ascending numbers along the diagonal are also terms of the even principal diagonal of a 2n X 2n spiral (A137928). - Avi Friedlich, May 21 2015
LINKS
Vincenzo Librandi, Rows n = 1..100, flattened
EXAMPLE
Triangle begins
10;
16, 26;
22, 36, 50;
28, 46, 64, 82;
34, 56, 78, 100, 122;
40, 66, 92, 118, 144, 170;
46, 76, 106, 136, 166, 196, 226;
52, 86, 120, 154, 188, 222, 256, 290;
58, 96, 134, 172, 210, 248, 286, 324, 362;
64, 106, 148, 190, 232, 274, 316, 358, 400, 442;
MAPLE
seq(seq( 2*(2*n*k+n+k+1), k=1..n), n=1..15) # G. C. Greubel, Mar 21 2021
MATHEMATICA
T[n_, k_]:=4*n*k + 2*n + 2*k + 2; Table[T[n, k], {n, 11}, {k, n}]//Flatten (* Vincenzo Librandi, Nov 21 2012 *)
PROG
(Magma) [4*n*k + 2*n + 2*k + 2: k in [1..n], n in [1..11]]; // Vincenzo Librandi, Nov 21 2012
(Sage) flatten([[2*(2*n*k+n+k+1) for k in (1..n)] for n in (1..15)]) # G. C. Greubel, Mar 21 2021
CROSSREFS
KEYWORD
AUTHOR
Vincenzo Librandi, Jan 21 2009
EXTENSIONS
Edited by Robert Hochberg, Jun 21 2010
STATUS
approved