A193043 Listed by antidiagonals, array A[k,n] = digital root of n-th nonzero k-gonal number.

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

Offset: 1

Author

Jonathan Vos Post, Aug 15 2011

Keywords

• nonn
• easy
• tabl
• base

Comments

The main diagonal begins 1, 4, 3, 1, 1, 6, 1, 7.

Examples

			The array begins:
===================================================
....|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=8|comment
====|===|===|===|===|===|===|===|===|==============
k=3.|.1.|.3.|.6.|.1.|.6.|.3.|.1.|.9.|
k=4.|.1.|.4.|.9.|.7.|.7.|.9.|.4.|.1.|
k=5.|.1.|.5.|.3.|.4.|.8.|.6.|.7.|.2.|A193090
k=6.|.1.|.6.|.6.|.1.|.9.|.3.|.1.|.3.|
k=7.|.1.|.7.|.9.|.7.|.1.|.9.|.4.|.4.|
k=8.|.1.|.8.|.3.|.4.|.2.|.6.|.7.|.5.|
k=9.|.1.|.9.|.6.|.1.|.3.|.3.|.1.|.6.|
k=10|.1.|.1.|.9.|.7.|.4.|.9.|.4.|.7.|
===================================================
		

Links

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

Crossrefs

Cf. A010888, A193090.

Programs

Mathematica

dr[n_]:=1+Mod[n-1,9]; A[k_,n_]:=dr[n*(n*(k-2)-(k-4))/2]; Flatten[Table[A[d-i+3,i],{d,13},{i,d}]] (* Ray Chandler, Aug 16 2011 *)

Extensions

Corrected and extended by Ray Chandler, Aug 16 2011