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A077339
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Triangle in which n-th row contains the first n numbers beginning with n.
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6
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1, 2, 20, 3, 30, 31, 4, 40, 41, 42, 5, 50, 51, 52, 53, 6, 60, 61, 62, 63, 64, 7, 70, 71, 72, 73, 74, 75, 8, 80, 81, 82, 83, 84, 85, 86, 9, 90, 91, 92, 93, 94, 95, 96, 97, 10, 100, 101, 102, 103, 104, 105, 106, 107, 108, 11, 110, 111, 112, 113, 114, 115, 116, 117, 118
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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COMMENTS
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Repetitions are allowed.
The first term in row m is T(m,1)=m, followed by T(m,2)=10m, 10m+1,..., 10m+9; then, T(m,12)=100m, 100m+1, ..., 100m+99, then T(m,112)=1000m,...,1000m+999, etc. (as long as the second index does not exceed the first, given the definition of this triangular sequence. But in principle one can consider the n-th number "starting with m" without that restriction). The first repetitions to occur seem to be T(20,1)=20=T(2,2), T(30,1)=30=T(3,2), T(31,1)=31=T(3,3), ... These cause the differences with A077341, and also the differences between A077340 and A077343. - M. F. Hasler, Jan 07 2013
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LINKS
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EXAMPLE
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The triangle starts:
1;
2, 20;
3, 30, 31;
4, 40, 41, 42;
5, 50, 51, 52, 53;
6, 60, 61, 62, 63, 64;
7, 70, 71, 72, 73, 74, 75;
8, 80, 81, 82, 83, 84, 85, 86;
9, 90, 91, 92, 93, 94, 95, 96, 97;
10, 100, 101, 102, 103, 104, 105, 106, 107, 108;
11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119;
12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 1200; ...
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PROG
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(PARI) A077339(m, n, p=1)={!n & n=m+(1-m=(sqrtint(8*m-7)+1)\2)*m\2; while(n>p, n-=p; p*=10); p*m+n-1} \\ returns the n-th number starting with m, allowing also n>m (useful for A077341 ff), or the m-th term of the sequence, if no 2nd arg is given. \\ - M. F. Hasler, Jan 07 2013
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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