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A036238
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Triangle of numbers a(r,j) = j*(j+1) mod r+2, r>=1, j=1..r.
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1
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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
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OFFSET
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1,1
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COMMENTS
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Called Dudley Triangle after the American mathematician and writer Underwood Dudley (b. 1937). - Amiram Eldar, Jun 10 2021
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REFERENCES
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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.
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LINKS
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EXAMPLE
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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;
...
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MATHEMATICA
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Table[Mod[j (j + 1), r + 2], {r, 14}, {j, r}] // Flatten (* Michael De Vlieger, Sep 23 2015 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Mar 31 2000
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STATUS
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approved
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