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

1,3

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.

Links

Table of n, a(n) for n=1..91.

Eric W. Weisstein, Digital Root

Eric W. Weisstein, Centered Polygonal Number

Example

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.|
=====================================

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 *)

Crossrefs

Cf. A086272, A086273, A010888, A193043.

Sequence in context: A265602 A185373 A244759 * A061642 A143313 A132588

Adjacent sequences: A194124 A194125 A194126 * A194128 A194129 A194130

Keyword

nonn,easy,base

Author

Jonathan Vos Post, Aug 15 2011

Extensions

Extended by Ray Chandler, Aug 16 2011

Status

approved