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

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

Offset: 1

Author

Jonathan Vos Post, Aug 15 2011

Keywords

• nonn
• easy
• base

Comments

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.

Examples

			The array begins:
=====================================
....|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=8|
====|===|===|===|===|===|===|===|===|
k=3.|.1.|.4.|.1.|.1.|.4.|.1.|.1.|.4.|
k=4.|.1.|.5.|.4.|.7.|.5.|.7.|.4.|.5.|
k=5.|.1.|.6.|.7.|.4.|.6.|.4.|.7.|.6.|
k=6.|.1.|.7.|.1.|.1.|.7.|.1.|.1.|.7.|
k=7.|.1.|.8.|.4.|.7.|.8.|.7.|.4.|.8.|
k=8.|.1.|.9.|.7.|.4.|.9.|.4.|.7.|.9.|
k=9.|.1.|.1.|.1.|.1.|.1.|.1.|.1.|.1.|
k=10|.1.|.2.|.4.|.7.|.2.|.7.|.4.|.2.|
=====================================
		

Links

• Eric W. Weisstein, Digital Root
• Eric W. Weisstein, Centered Polygonal Number

Crossrefs

Cf. A086272, A086273, A010888, A193043.

Programs

Mathematica

dr[n_]:=1+Mod[n-1, 9]; A[k_,n_]:=dr[k*n*(n-1)/2+1];
Flatten[Table[A[d-i+3, i], {d, 13}, {i, d}]] (* Ray Chandler, Aug 16 2011 *)

Extensions

Extended by Ray Chandler, Aug 16 2011