cp's OEIS Frontend

A194127 Listed by antidiagonals, array A(k,n) = digital root of n-th nonzero centered k-gonal number.

%I A194127 #17 Feb 16 2025 08:33:15
%S A194127 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 A194127 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 A194127 1,4,2,1,7,8,1,1,5,1,1,6,4,1,3,7,1,9,1,1,6,4,1
%N A194127 Listed by antidiagonals, array A(k,n) = digital root of n-th nonzero centered k-gonal number.
%C A194127 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 A194127 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>
%H A194127 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/CenteredPolygonalNumber.html">Centered Polygonal Number</a>
%e A194127 The array begins:
%e A194127 =====================================
%e A194127 ....|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=8|
%e A194127 ====|===|===|===|===|===|===|===|===|
%e A194127 k=3.|.1.|.4.|.1.|.1.|.4.|.1.|.1.|.4.|
%e A194127 k=4.|.1.|.5.|.4.|.7.|.5.|.7.|.4.|.5.|
%e A194127 k=5.|.1.|.6.|.7.|.4.|.6.|.4.|.7.|.6.|
%e A194127 k=6.|.1.|.7.|.1.|.1.|.7.|.1.|.1.|.7.|
%e A194127 k=7.|.1.|.8.|.4.|.7.|.8.|.7.|.4.|.8.|
%e A194127 k=8.|.1.|.9.|.7.|.4.|.9.|.4.|.7.|.9.|
%e A194127 k=9.|.1.|.1.|.1.|.1.|.1.|.1.|.1.|.1.|
%e A194127 k=10|.1.|.2.|.4.|.7.|.2.|.7.|.4.|.2.|
%e A194127 =====================================
%t A194127 dr[n_]:=1+Mod[n-1, 9]; A[k_,n_]:=dr[k*n*(n-1)/2+1];
%t A194127 Flatten[Table[A[d-i+3, i], {d, 13}, {i, d}]] (* Ray Chandler, Aug 16 2011 *)
%Y A194127 Cf. A086272, A086273, A010888, A193043.
%K A194127 nonn,easy,base
%O A194127 1,3
%A A194127 _Jonathan Vos Post_, Aug 15 2011
%E A194127 Extended by _Ray Chandler_, Aug 16 2011