A036238 Triangle of numbers a(r,j) = j*(j+1) mod r+2, r>=1, j=1..r.

2, 2, 2, 2, 1, 2, 2, 0, 0, 2, 2, 6, 5, 6, 2, 2, 6, 4, 4, 6, 2, 2, 6, 3, 2, 3, 6, 2, 2, 6, 2, 0, 0, 2, 6, 2, 2, 6, 1, 9, 8, 9, 1, 6, 2, 2, 6, 0, 8, 6, 6, 8, 0, 6, 2, 2, 6, 12, 7, 4, 3, 4, 7, 12, 6, 2, 2, 6, 12, 6, 2, 0, 0, 2, 6, 12, 6, 2, 2, 6, 12, 5, 0, 12, 11, 12, 0, 5, 12, 6, 2, 2, 6, 12, 4, 14, 10, 8, 8, 10, 14, 4, 12, 6, 2

Offset

1,1

Comments

Called Dudley Triangle after the American mathematician and writer Underwood Dudley (b. 1937). - Amiram Eldar, Jun 10 2021

Central terms are A014682(n), n>0. - Philippe Deléham, May 11 2023

References

Clifford A. Pickover, The Dudley Triangle", Ch. 59 in Wonders of Numbers: Adventures in Mathematics, Mind, and Meaning, Oxford, England: Oxford University Press, 2001, pp. 144-145.

Links

Alois P. Heinz, Rows n = 1..200, flattened

Underwood Dudley, Problem 1277: An infinite triangular array, Math. Mag., Vol. 60, No. 5 (1987), p. 328.

Wikipedia, Dudley triangle.

Example

Triangle starts:
  2;
  2, 2;
  2, 1, 2;
  2, 0, 0, 2;
  2, 6, 5, 6, 2;
  2, 6, 4, 4, 6, 2;
  2, 6, 3, 2, 3, 6, 2;
  ...

Mathematica

Table[Mod[j (j + 1), r + 2], {r, 14}, {j, r}] // Flatten (* Michael De Vlieger, Sep 23 2015 *)

Prog

(C) #include <stdio.h> #include <stdlib.h> #define MAX_ROWS 100 #define USAGE "Usage: 'A036238 num' where num is the last row of the triangle to compute\n" int main(int argc, char *argv[]) { unsigned long i, j, end, ans; if (argc < 2) { fprintf(stderr, USAGE); return EXIT_FAILURE; } end = atoi(argv[1]); end = (end >= MAX_ROWS) ? MAX_ROWS: end; fprintf(stdout, "Values: "); for (i = 1; i <= end; i++) { for (j = 1; j <= i; j++) { ans = j * (j + 1) % (i +2); fprintf(stdout, "%ld, ", ans); } } fprintf(stdout, "\n"); return EXIT_SUCCESS; } /* Larry Reeves (larryr(AT)acm.org), Mar 31 2000 */
(PARI) tabl(nn) = {for (n=1, nn, for (k=1, n, print1(k*(k+1) % (n+2), ", "); ); print(); ); } \\ Michel Marcus, Sep 23 2015

Crossrefs

Cf. A014682.

Sequence in context: A232800 A248380 A090044 * A318723 A225180 A276134

Adjacent sequences: A036235 A036236 A036237 * A036239 A036240 A036241

Keyword

nonn,look,easy,tabl

Author

N. J. A. Sloane.

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Mar 31 2000

Status

approved