A117511 Triangular numbers for which the sum of the digits equals the sum of the digits of the next triangular number.

36, 153, 2556, 3240, 4851, 5778, 9045, 11628, 13041, 14535, 17766, 19503, 33930, 41328, 46665, 49455, 52326, 71253, 74691, 81810, 85491, 93096, 109278, 122265, 131328, 140715, 145530, 160461, 170820, 181503, 186966, 192510, 203841, 252405, 258840, 265356

Offset: 1

Author

Luc Stevens (lms022(AT)yahoo.com), Apr 26 2006

Keywords

• base
• nonn
• changed

Comments

Each term is divisible by 9.

Examples

			153 is in the sequence because (1) 153 is triangular number a(18), triangular number a(19)=171 and (2) 1+5+3=1+7+1.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000217, A004157.

Programs

Mathematica

Transpose[With[{c=Partition[Accumulate[Range[2000]],2,1]}, Select[c, Total[IntegerDigits[First[#]]]==Total[IntegerDigits[Last[#]]]&]]] [[1]] (* Harvey P. Dale, Oct 18 2011 *)
(#(#+1))/2&/@(SequencePosition[Total[IntegerDigits[#]]&/@Accumulate[ Range[ 1000]],{x_,x_}][[All,1]]) (* Harvey P. Dale, Mar 02 2022 *)

Formula

s(a(n)) = s(a(n+1)), where s(n) is the sum of the digits of n.

Extensions

Corrected by Harvey P. Dale, Oct 18 2011