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A077339 Triangle in which n-th row contains the first n numbers beginning with n. 6
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)
OFFSET

1,2

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

LINKS

Table of n, a(n) for n=1..65.

EXAMPLE

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; ...

PROG

(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

CROSSREFS

Cf. A077340. Different from A077341.

Sequence in context: A220943 A082259 A342077 * A077341 A344545 A076495

Adjacent sequences:  A077336 A077337 A077338 * A077340 A077341 A077342

KEYWORD

base,easy,nonn,tabl

AUTHOR

Amarnath Murthy, Nov 05 2002

EXTENSIONS

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

STATUS

approved

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Last modified October 17 15:49 EDT 2021. Contains 348065 sequences. (Running on oeis4.)