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A145389
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Digital roots of triangular numbers.
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6
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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; internal format)
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OFFSET
| 0,3
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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)).
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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 [From Paolo P. Lava (paoloplava(AT)gmail.com), Oct 14 2008]
GF for n>0: 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)) added by Ant King, Nov 16 2010.
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MATHEMATICA
| digitalRoot[n_Integer?Positive] := FixedPoint[Plus@@IntegerDigits[#]&, n]; Table[If[n==0, 0, digitalRoot[n(n+1)/2]], {n, 0, 100}] (* From Vladimir Joseph Stephan Orlovsky, May 02 2011 *)
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CROSSREFS
| Cf. A000217, A004157, A010888.
Sequence in context: A078768 A089078 A134804 * A055263 A004157 A091068
Adjacent sequences: A145386 A145387 A145388 * A145390 A145391 A145392
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KEYWORD
| nonn,base,easy
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 10 2008
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