OFFSET
1,3
COMMENTS
All triangular numbers have a digital root of 1,3,6 or 9 (except for the number 0). So this sequence contains all triangular numbers except those which have digital root 9.
FORMULA
Empirical g.f.: -x^2*(x^14 +2*x^13 +3*x^12 +4*x^11 +5*x^10 +6*x^9 +7*x^8 +25*x^7 +7*x^6 +6*x^5 +5*x^4 +4*x^3 +3*x^2 +2*x +1) / ((x -1)^3*(x^6 +x^5 +x^4 +x^3 +x^2 +x +1)^2). - Colin Barker, Jan 17 2014
Sum_{n>=2} 1/a(n) = 2*cot(Pi/9)*Pi/9. - Amiram Eldar, Sep 15 2022
EXAMPLE
2926 is in the sequence because (1) it is a triangular number and (2) the digital root is 1, which is a triangular number.
MATHEMATICA
drt9Q[n_]:=NestWhile[Total[IntegerDigits[#]]&, n, #>9&]!=9; Select[ Accumulate[ Range[0, 100]], drt9Q] (* Harvey P. Dale, Jan 23 2012 *)
t[n_] := n*(n + 1)/2; Join[{0}, t /@ Table[9*n + Range[7], {n, 0, 10}] // Flatten] (* Amiram Eldar, Sep 15 2022 *)
CROSSREFS
KEYWORD
easy,nonn,base
AUTHOR
Luc Stevens (lms022(AT)yahoo.com), Apr 28 2006
STATUS
approved