A194127 - OEIS

%I #16 Mar 30 2012 18:40:59

%S 1,1,4,1,5,1,1,6,4,1,1,7,7,7,4,1,8,1,4,5,1,1,9,4,1,6,7,1,1,1,7,7,7,4,

%T 4,4,1,2,1,4,8,1,7,5,1,1,3,4,1,9,7,1,6,1,1,1,4,7,7,1,4,4,7,1,1,4,1,5,

%U 1,4,2,1,7,8,1,1,5,1,1,6,4,1,3,7,1,9,1,1,6,4,1

%N Listed by antidiagonals, array A(k,n) = digital root of n-th nonzero centered k-gonal number.

%C This is to centered k-gonal numbers as A193043 is to k-gonal numbers.  The main diagonal begins: 1, 5, 7, 1, 8, 4, 1, 2.

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Number</a>

%e The array begins:

%e =====================================

%e ....|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=8|

%e ====|===|===|===|===|===|===|===|===|

%e k=3.|.1.|.4.|.1.|.1.|.4.|.1.|.1.|.4.|

%e k=4.|.1.|.5.|.4.|.7.|.5.|.7.|.4.|.5.|

%e k=5.|.1.|.6.|.7.|.4.|.6.|.4.|.7.|.6.|

%e k=6.|.1.|.7.|.1.|.1.|.7.|.1.|.1.|.7.|

%e k=7.|.1.|.8.|.4.|.7.|.8.|.7.|.4.|.8.|

%e k=8.|.1.|.9.|.7.|.4.|.9.|.4.|.7.|.9.|

%e k=9.|.1.|.1.|.1.|.1.|.1.|.1.|.1.|.1.|

%e k=10|.1.|.2.|.4.|.7.|.2.|.7.|.4.|.2.|

%e =====================================

%t dr[n_]:=1+Mod[n-1, 9]; A[k_,n_]:=dr[k*n*(n-1)/2+1];

%t Flatten[Table[A[d-i+3, i], {d, 13}, {i, d}]] (* Ray Chandler, Aug 16 2011 *)

%Y Cf. A086272, A086273, A010888, A193043.

%K nonn,easy,base

%O 1,3

%A _Jonathan Vos Post_, Aug 15 2011

%E Extended by _Ray Chandler_, Aug 16 2011