cp's OEIS Frontend

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

%I A193043 #23 Feb 16 2025 08:33:15
%S A193043 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,
%T A193043 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,
%U A193043 6,4,4,3,7,4,9,1,4,6,1,5,9,1,5,9,1,5,9,1,5,9,1
%N A193043 Listed by antidiagonals, array A[k,n] = digital root of n-th nonzero k-gonal number.
%C A193043 The main diagonal begins 1, 4, 3, 1, 1, 6, 1, 7.
%H A193043 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/PolygonalNumber.html">Polygonal Number</a>
%H A193043 Eric W. Weisstein, <a href="https://mathworld.wolfram.com/DigitalRoot.html">Digital Root</a>
%e A193043 The array begins:
%e A193043 ===================================================
%e A193043 ....|n=1|n=2|n=3|n=4|n=5|n=6|n=7|n=8|comment
%e A193043 ====|===|===|===|===|===|===|===|===|==============
%e A193043 k=3.|.1.|.3.|.6.|.1.|.6.|.3.|.1.|.9.|
%e A193043 k=4.|.1.|.4.|.9.|.7.|.7.|.9.|.4.|.1.|
%e A193043 k=5.|.1.|.5.|.3.|.4.|.8.|.6.|.7.|.2.|A193090
%e A193043 k=6.|.1.|.6.|.6.|.1.|.9.|.3.|.1.|.3.|
%e A193043 k=7.|.1.|.7.|.9.|.7.|.1.|.9.|.4.|.4.|
%e A193043 k=8.|.1.|.8.|.3.|.4.|.2.|.6.|.7.|.5.|
%e A193043 k=9.|.1.|.9.|.6.|.1.|.3.|.3.|.1.|.6.|
%e A193043 k=10|.1.|.1.|.9.|.7.|.4.|.9.|.4.|.7.|
%e A193043 ===================================================
%t A193043 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 *)
%Y A193043 Cf. A010888, A193090.
%K A193043 nonn,easy,tabl,base
%O A193043 1,3
%A A193043 _Jonathan Vos Post_, Aug 15 2011
%E A193043 Corrected and extended by _Ray Chandler_, Aug 16 2011