A173233 -id:A173233 - cp's OEIS frontend

A174233 Triangle T(n,k) read by rows: the numerator of 1/n^2 - 1/(k-n)^2, 0 <= k < 2n.

0, -1, 0, -3, -1, -3, 0, -5, -8, -1, -8, -5, 0, -7, -3, -15, -1, -15, -3, -7, 0, -9, -16, -21, -24, -1, -24, -21, -16, -9, 0, -11, -5, -1, -2, -35, -1, -35, -2, -1, -5, -11, 0, -13, -24, -33, -40, -45, -48, -1, -48, -45, -40, -33, -24, -13, 0, -15, -7, -39, -3, -55, -15, -63

Offset: 1

Paul Curtz, Mar 13 2010

A value of -1 is substituted at the poles where k=n.
The triangle is created by selecting the first 2, 4, 6 etc elements of the array shown in A172370, equivalent to attaching the initial elements of the rows of A172157 to the rows of A174190.
If the first column of zeros is removed from the triangle, each row is left-right symmetric with respect to the center value.

			The triangle starts
  0,  -1;
  0,  -3,  -1,  -3;
  0,  -5,  -8,  -1,  -8,  -5;
  0,  -7,  -3, -15,  -1, -15,  -3,  -7;
  0,  -9, -16, -21, -24,  -1, -24, -21, -16,  -9;
  0, -11,  -5,  -1,  -2, -35,  -1, -35,  -2,  -1,  -5, -11;
  0, -13, -24, -33, -40, -45, -48,  -1, -48, -45, -40, -33, -24, -13;

G. C. Greubel, Rows n=1..100 of triangle, flattened

Cf. A175779, A172370, A061035, A174190, A120072.

A173233 := proc(n,k) if k = n then -1 ; else 1/n^2-1/(k-n)^2 ; numer(%) ; end if; end proc: # R. J. Mathar, Jan 06 2011

T[n_, n_] := -1; T[n_, k_] := 1/n^2 - 1/(k - n)^2; Table[Numerator[T[n, k]], {n, 1, 20}, {k, 0, 2 n - 1}]//Flatten (* G. C. Greubel, Sep 19 2018 *)

A173232 Numbers k such that k and k+2 are both members of A002822.

Original entry on oeis.org

1, 3, 5, 10, 23, 30, 38, 45, 70, 135, 170, 175, 213, 215, 268, 355, 465, 560, 588, 653, 703, 705, 710, 773, 798, 835, 940, 978, 1115, 1130, 1158, 1258, 1370, 1500, 1570, 1843, 1860, 2040, 2280, 2285, 2333, 2425, 2985, 3008, 3020, 3598, 3600, 3838, 4375, 4450, 4480

Offset: 1

Juri-Stepan Gerasimov, Feb 13 2010

nonn

			a(1)=1 because 1 and 3 are both in A002822.

Cf. A002822, A173233.

isokp(n) = isprime(6*n-1) && isprime(6*n+1);
isok(k) = isokp(k) && isokp(k+2); \\ Michel Marcus, May 15 2020

Definition corrected, and sequence corrected (1158 inserted) by R. J. Mathar, May 02 2010

More terms from Jinyuan Wang, May 15 2020

cp's OEIS Frontend

A174233 Triangle T(n,k) read by rows: the numerator of 1/n^2 - 1/(k-n)^2, 0 <= k < 2n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica