A077339 Triangle in which n-th row contains the first n numbers beginning with n.

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

Offset: 1

Author

Amarnath Murthy, Nov 05 2002

Keywords

• base
• easy
• nonn
• tabl

Comments

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

Examples

			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; ...
		

Crossrefs

Cf. A077340. Different from A077341.

Programs

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

Extensions

Edited by N. J. A. Sloane, Jun 12 2007