Revision History for A081521
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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| A081521
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Triangle read by rows: row n contains n terms in increasing order, relatively prime to n, whose sum is a multiple of n and such that the row contains the smallest possible subset of consecutive numbers starting with 1.
(history;
published version)
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#16 by Peter Luschny at Sun May 24 04:02:29 EDT 2020
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#15 by Peter Luschny at Sun May 24 04:02:22 EDT 2020
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| EXTENSIONS
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MoreName corrected and more terms from Jinyuan Wang, May 24 2020
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#14 by Jinyuan Wang at Sun May 24 00:01:25 EDT 2020
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| NAME
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Triangle read by rows: row n contains n terms in increasing order, relatively prime to n, whose sum is a multiple of n and such that the row contains the largestsmallest possible subset of consecutive numbers starting with 1.
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| DATA
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1, 1, 3, 1, 4, 7, 1, 3, 5, 7, 1, 2, 3, 6, 8, 1, 5, 7, 11, 13, 17, 1, 2, 3, 4, 5, 8, 12, 1, 3, 5, 7, 9, 11, 13, 15, 1, 2, 4, 5, 7, 8, 10, 13, 22, 1, 3, 7, 9, 11, 13, 17, 19, 21, 29, 1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 20
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| PROG
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(PARI) row(n) = {my(m=n*(n-1)/2, v); forstep(k=m+n/(2-n%2), oo, n, v=List([]); for(i=2, k-m, if(gcd(n, i)==1, listput(v, i))); if(#v>n-2, forsubset([#v, n-1], w, if(r=1+sum(i=1, n-1, v[w[i]])==k, return(concat(1, vector(n-1, i, v[w[i]]))))))); } \\ Jinyuan Wang, May 24 2020
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| KEYWORD
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more,nonn,tabl,more
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| EXTENSIONS
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More terms from Jinyuan Wang, May 24 2020
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| STATUS
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approved
editing
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Discussion
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| Sun May 24
| 01:56
| Michel Marcus: needs extension Name corrected by
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#13 by Susanna Cuyler at Sun Nov 24 09:58:20 EST 2019
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#12 by Joerg Arndt at Sun Nov 24 04:03:58 EST 2019
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#11 by Michel Marcus at Sun Nov 24 04:03:23 EST 2019
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#10 by Michel Marcus at Sun Nov 24 04:03:14 EST 2019
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| EXAMPLE
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Triangle begins:
1;
1,, 3;
1,, 4,, 7;
1,, 3,, 5,, 7;
1,, 2,, 3,, 6,, 8;
1,, 5,, 7,, 11,, 13,, 17;
1,, 2,, 3,, 4,, 5,, 8,, 12; ...;
...
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| STATUS
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proposed
editing
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#9 by Joerg Arndt at Sun Nov 24 04:01:12 EST 2019
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#8 by Joerg Arndt at Sun Nov 24 04:00:55 EST 2019
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| EXAMPLE
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1; 1,3; 1,4,7; 1,3,5,7; 1,2,3,6,8; 1,5,7,11,13,17; 1,2,3,4,5,8,12; ...
1;
1,3;
1,4,7;
1,3,5,7;
1,2,3,6,8;
1,5,7,11,13,17;
1,2,3,4,5,8,12; ...
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proposed
editing
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#7 by Michel Marcus at Sun Nov 24 03:19:11 EST 2019
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