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A117520 Triangular numbers for which the digital root is also a triangular number. 0
0, 1, 3, 6, 10, 15, 21, 28, 55, 66, 78, 91, 105, 120, 136, 190, 210, 231, 253, 276, 300, 325, 406, 435, 465, 496, 528, 561, 595, 703, 741, 780, 820, 861, 903, 946, 1081, 1128, 1176, 1225, 1275, 1326, 1378, 1540, 1596, 1653, 1711, 1770, 1830, 1891, 2080, 2145 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..52.

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

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 *)

CROSSREFS

Cf. A000217.

Sequence in context: A025730 A066353 A179653 * A147846 A062099 A115650

Adjacent sequences:  A117517 A117518 A117519 * A117521 A117522 A117523

KEYWORD

easy,nonn,base

AUTHOR

Luc Stevens (lms022(AT)yahoo.com), Apr 28 2006

STATUS

approved

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Last modified August 25 05:42 EDT 2019. Contains 326323 sequences. (Running on oeis4.)