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A141663 Regular triangle T(n,m) = abs(prime(n) - m^2), 0 <= m <= n-1. 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 (list; table; graph; refs; listen; history; text; internal format)
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
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
KEYWORD
nonn,easy,tabl
AUTHOR
Roger L. Bagula, Sep 05 2008
EXTENSIONS
Edited by Michel Marcus, Feb 01 2015
STATUS
approved

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Last modified June 22 22:20 EDT 2024. Contains 373619 sequences. (Running on oeis4.)