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A194127 Listed by antidiagonals, array A(k,n) = digital root of n-th nonzero centered k-gonal number. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 27 08:39 EDT 2021. Contains 347689 sequences. (Running on oeis4.)