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A117511
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Triangular numbers for which the sum of the digits equals the sum of the digits of the next triangular number.
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1
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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
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OFFSET
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1,1
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COMMENTS
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s(n) stands for the sum of the digits of n. Each number of the sequence is divisible by 9.
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LINKS
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FORMULA
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s(a(n))=s(a(n+1))
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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Luc Stevens (lms022(AT)yahoo.com), Apr 26 2006
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EXTENSIONS
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Corrected by Harvey P. Dale, Oct 18 2011
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STATUS
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approved
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