

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
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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+k1: k in [1..n], n in [1..11]]; /* or, see example: */ [[2*n*k+n+k1: k in [1..n]]: n in [1..9]]; // Bruno Berselli, Dec 04 2011
(PARI) T(n, k)=2*n*k+n+k1 \\ Charles R Greathouse IV, Dec 28 2011
(Sage) flatten([[2*n*k+n+n1 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



