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

1,1

Comments

Each term is divisible by 9.

Links

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

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A000217, A004157.

Sequence in context: A034592 A160754 A275496 * A250632 A211728 A211737

Adjacent sequences: A117508 A117509 A117510 * A117512 A117513 A117514

Keyword

base,nonn

Author

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

Extensions

Corrected by Harvey P. Dale, Oct 18 2011

Status

approved