A141663 Regular triangle T(n,m) = abs(prime(n) - m^2), 0 <= m <= n-1.

2, 3, 2, 5, 4, 1, 7, 6, 3, 2, 11, 10, 7, 2, 5, 13, 12, 9, 4, 3, 12, 17, 16, 13, 8, 1, 8, 19, 19, 18, 15, 10, 3, 6, 17, 30, 23, 22, 19, 14, 7, 2, 13, 26, 41, 29, 28, 25, 20, 13, 4, 7, 20, 35, 52, 31, 30, 27, 22, 15, 6, 5, 18, 33, 50, 69

Offset

1,1

Comments

Row sums are: {2, 5, 10, 18, 35, 53, 82, 118, 167, 233, 306}.

From Michel Marcus, Feb 01 2015: (Start)

For p>5, and when only the positive terms of p-m^2 are considered, one gets the following irregular triangle:

6, 3,

10, 7, 2,

12, 9, 4,

16, 13, 8, 1,

18, 15, 10, 3,

...

Then in each row, there are 2 integers a,b such that 1<a<b and a divides b (see Problem in links).

(End)

Links

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

David M. Bloom, Problem 1438, Mathematics Magazine, Vol. 67, No. 1 (Feb., 1994), p. 66.

Formula

T(n,m) = abs(prime(n) - m^2), 0 <= m <= n-1.

Example

Triangle begins
  { 2},
  { 3,  2},
  { 5,  4,  1},
  { 7,  6,  3,  2},
  {11, 10,  7,  2,  5},
  {13, 12,  9,  4,  3, 12},
  {17, 16, 13,  8,  1,  8, 19},
  {19, 18, 15, 10,  3,  6, 17, 30},
  {23, 22, 19, 14,  7,  2, 13, 26, 41},
  {29, 28, 25, 20, 13,  4,  7, 20, 35, 52},
  {31, 30, 27, 22, 15,  6,  5, 18, 33, 50, 69}

Mathematica

Clear[T, n, m] T[n_, m_] = Abs[Prime[n] - m^2]; Table[Table[T[n, m], {m, 0, n-1}], {n, 1, 10}]; Flatten[%]

Prog

(PARI) tabl(nn) = {for (n=1, nn, for (m=0, n-1, print1(abs(prime(n)-m^2), ", "); ); print(); ); } \\ Michel Marcus, Feb 01 2015

Crossrefs

Cf. A002378.

Sequence in context: A358462 A141465 A263216 * A011153 A214750 A317585

Adjacent sequences: A141660 A141661 A141662 * A141664 A141665 A141666

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Sep 05 2008

Extensions

Edited by Michel Marcus, Feb 01 2015

Status

approved