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

1,3

Comments

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

Links

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

Eric Weisstein's World of Mathematics, Polygonal Number.

Eric Weisstein's World of Mathematics, Digital Root.

Example

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

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 *)

Crossrefs

Cf. A010888, A086271, A193090.

Sequence in context: A307394 A194540 A351153 * A086271 A345229 A080851

Adjacent sequences: A193040 A193041 A193042 * A193044 A193045 A193046

Keyword

nonn,easy,tabl,base

Author

Jonathan Vos Post, Aug 15 2011

Extensions

Corrected and extended by Ray Chandler, Aug 16 2011

Status

approved