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A145389 Digital roots of triangular numbers. 7
0, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6, 3, 1, 9, 9, 1, 3, 6, 1, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A010888(A000217(n)).

Periodic sequence for n>0: a(n+9) = a(n);

a(A016777(n)) = 1; a(A007494(n)) <> 1;

a(A090570(n)) = A010888(A090570(n)).

LINKS

Table of n, a(n) for n=0..86.

FORMULA

a(n) = 1 + [(n^2+n-2)/2] mod 9. - Ant King, Apr 25 2009

a(n) = (1/108)*{13*(n mod 9)-83*[(n+1) mod 9]+37*[(n+2) mod 9]+49*[(n+3) mod 9]-47*[(n+4) mod 9]+73*[(n+5) mod 9]-23*[(n+6) mod 9]-11*[(n+7) mod 9]+109*[(n+8) mod 9]}-9*[C(2*n,n) mod 2], with n>=0. - Paolo P. Lava, Oct 14 2008

G.f.: x(1+3x+6x^2+x^3+6x^4+3x^5+x^6+9x^7+9x^8)/((1-x)(1+x+x^2)(1+x^3+x^6)). - Ant King, Nov 16 2010.

MATHEMATICA

digitalRoot[n_Integer?Positive] := FixedPoint[Plus@@IntegerDigits[#]&, n]; Table[If[n==0, 0, digitalRoot[n(n+1)/2]], {n, 0, 100}] (* Vladimir Joseph Stephan Orlovsky, May 02 2011 *)

PROG

(PARI) a(n)=if(n, n=n*(n+1)/2%9; if(n, n, 9), 0) \\ Charles R Greathouse IV, Dec 19 2016

CROSSREFS

Cf. A000217, A004157, A010888.

Sequence in context: A307281 A089078 A134804 * A055263 A004157 A091068

Adjacent sequences:  A145386 A145387 A145388 * A145390 A145391 A145392

KEYWORD

nonn,base,easy

AUTHOR

Reinhard Zumkeller, Oct 10 2008

STATUS

approved

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Last modified June 19 23:39 EDT 2019. Contains 324222 sequences. (Running on oeis4.)