Is this a staircase number?
R, 97 bytes



function(n)"if"(n&gt;1,{while({T=T+1;x=paste(c(1:T,T:2-1),collapse="");nchar(x)&lt;nchar(n)})0;x==n},T)


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Takes n as a character or an integer; using character will give correct results for integers that can't be held precisely as a 64-bit double.

Generates staircase numbers until it finds one at least as long as n is, then tests for equality.

Equivalent to:

function(n)
    if(n > 1){
        T &lt;- T + 1
        x &lt;- paste(c(1:T,T:2-1),collapse="")
        while(nchar(x) &lt; nchar(n)){
            T &lt;- T + 1
            x &lt;- paste(c(1:T,T:2-1),collapse="")
        }
        return(x == n)
    } else
        return(TRUE)