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A155151 Triangle read by rows: T(m, n) = 4mn + 2m + 2n + 2, where m is the row and n is the position in the row, for 1 <= n <= m. 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(m,n)=2^p with p prime, then 2^p-1 = 4mn + 2m + 2n + 1 = (2m+1)*(2n+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(m,n) = 2*A144650(m,n).

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;

MATHEMATICA

t[n_, k_]:=4 n*k + 2n + 2k + 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

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 October 26 08:06 EDT 2020. Contains 338027 sequences. (Running on oeis4.)