Curious numbers as sum of two Narayana's cows numbers
This paper aims to identify all curious numbers that can be represented as the sum of two Narayana's cows numbers.Narayana's cows sequence satisfies the third-order linear recurrence relation Nn=Nn-1 +Nn-3,n≥3 and n0=0,N1=N2=1.For the problem of the sum of Narayana's cows numbers being a curious num-bers,a corresponding Diophantine equation is established.Different forms of the equation are arranged,and a larger upper bound for each unknown variable is obtained through linear forms in logarithms.Then,using the reduction method,the upper bound of each unknown variable is reduced to a computable upper bound.Final-ly,based on the computable upper bound of the unknown variables,Mathematica is used to find all curious numbers expressible as the sum of two Narayana's cows numbers.
Narayana's cows sequencerepdigitscurious numberslinear forms in logarithmsreduction method
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