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A155151 Triangle T(n, k) = 4*n*k + 2*n + 2*k + 2, read by rows. 4
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, 70, 116, 162 (list; table; graph; refs; listen; history; text; internal format)
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

FORMULA

T(n, k) = 2*A144650(n, k).

Sum_{k=1..n} T(n,k) = n*(2*n^2 + 5*n + 3) = n*A014105(n+2) =

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

Cf. A000043, A000668, A016957, A017029, A017341, A054723, A082286, A144650.

Sequence in context: A187397 A152138 A109100 * A104788 A249720 A080360

Adjacent sequences: A155148 A155149 A155150 * A155152 A155153 A155154

KEYWORD

nonn,tabl,easy

AUTHOR

Vincenzo Librandi, Jan 21 2009

EXTENSIONS

Edited by Robert Hochberg, Jun 21 2010

STATUS

approved

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Last modified December 2 18:40 EST 2022. Contains 358510 sequences. (Running on oeis4.)