|
%I #18 Apr 30 2015 17:51:37
%S 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,
%T 73,74,75,8,80,81,82,83,84,85,86,9,90,91,92,93,94,95,96,97,10,100,101,
%U 102,103,104,105,106,107,108,11,110,111,112,113,114,115,116,117,118
%N Triangle in which n-th row contains the first n numbers beginning with n.
%C Repetitions are allowed.
%C 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
%e The triangle starts:
%e 1;
%e 2, 20;
%e 3, 30, 31;
%e 4, 40, 41, 42;
%e 5, 50, 51, 52, 53;
%e 6, 60, 61, 62, 63, 64;
%e 7, 70, 71, 72, 73, 74, 75;
%e 8, 80, 81, 82, 83, 84, 85, 86;
%e 9, 90, 91, 92, 93, 94, 95, 96, 97;
%e 10, 100, 101, 102, 103, 104, 105, 106, 107, 108;
%e 11, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119;
%e 12, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 1200; ...
%o (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
%Y Cf. A077340. Different from A077341.
%K base,easy,nonn,tabl
%O 1,2
%A _Amarnath Murthy_, Nov 05 2002
%E Edited by _N. J. A. Sloane_, Jun 12 2007
|
