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A144562 Triangle read by rows: T(n, k) = 2*n*k + n + k - 1. 34
3, 6, 11, 9, 16, 23, 12, 21, 30, 39, 15, 26, 37, 48, 59, 18, 31, 44, 57, 70, 83, 21, 36, 51, 66, 81, 96, 111, 24, 41, 58, 75, 92, 109, 126, 143, 27, 46, 65, 84, 103, 122, 141, 160, 179, 30, 51, 72, 93, 114, 135, 156, 177, 198, 219, 33, 56, 79, 102, 125, 148, 171, 194 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Rearrangement of A153238, numbers n such that 2*n+3 is not prime (we have 2*T(n,k) + 3 = (2*n+1)*(2*k+1), as 2*n+3 is odd it consists of (at least) two odd factors and all such factors appear by definition).

LINKS

Vincenzo Librandi, Rows n = 1..100, flattened

Mutsumi Suzuki Vincenzo Librandi's method for sequential primes (Librandi's description in Italian).

FORMULA

Sum_{k=1..n} T(n,k) = n*(2*n^2 + 5*n - 1)/2 = A144640(n). - G. C. Greubel, Mar 01 2021

EXAMPLE

Triangle begins:

   3;

   6, 11;

   9, 16, 23;

  12, 21, 30, 39;

  15, 26, 37, 48,  59;

  18, 31, 44, 57,  70,  83;

  21, 36, 51, 66,  81,  96, 111;

  24, 41, 58, 75,  92, 109, 126, 143;

  27, 46, 65, 84, 103, 122, 141, 160, 179;

MAPLE

A144562:= (n, k) -> 2*n*k +n +k -1; seq(seq(A144562(n, k), k=1..n), n=1..12); # G. C. Greubel, Mar 01 2021

MATHEMATICA

T[n_, k_]:= 2*n*k +n +k -1; Table[T[n, k], {n, 11}, {k, n}]//Flatten

PROG

(MAGMA) [2*n*k+n+k-1: k in [1..n], n in [1..11]]; /* or, see example: */ [[2*n*k+n+k-1: k in [1..n]]: n in [1..9]]; // Bruno Berselli, Dec 04 2011

(PARI) T(n, k)=2*n*k+n+k-1 \\ Charles R Greathouse IV, Dec 28 2011

(Sage) flatten([[2*n*k+n+n-1 for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Mar 01 2021

CROSSREFS

Cf. A067076, A142463, A144640, A153238.

Sequence in context: A006509 A325551 A258928 * A102889 A183543 A256108

Adjacent sequences:  A144559 A144560 A144561 * A144563 A144564 A144565

KEYWORD

nonn,easy,tabl

AUTHOR

Vincenzo Librandi, Jan 06 2009

EXTENSIONS

Edited by Ray Chandler, Jan 07 2009

STATUS

approved

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Last modified April 15 13:13 EDT 2021. Contains 342977 sequences. (Running on oeis4.)