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The base idea is the same as the previous program: find a square near our target number, and represent its root and the remainder recursively. … But now we allow our square being also some larger than the target number, which then makes the remainder negative. …

Ceylon (on JVM), 92 87 78 bytes (The Big integer type Whole which is used here does only exist on the JVM, not when compiling for JavaScript.) This is the third improvement (78 bytes): import ceylo …

((any(s*.letter) then 11 else 2) .. 36) // map each r of them to ... .map((r) => // try parsing s as a number using base r parseInteger(s, r) // if that …

any(formatInteger(n,16)*.digit); Straightforward ... we format n as a hexadecimal number (which produces a string), call on each character of that string the .digit number (which returns true if it is …

Ceylon, 90 bytes alias I=>Integer;I x(I a,I b)=>[for(i in 0:64)if(b.get(i))a*2^i].fold(0)((y,z)=>y.xor(z)); This is just the algorithm as described: multiply a by 2^i wherever the ith bit is set in …

Ceylon, 111111111111111111111111111111111111111111 (42 digits) This was my second try: shared void run(){print("1".repeat(42));} A program with length 41, prints a string of 42 ones. My first, …

. => // increment the counter, then check if it // is an unspeakable number. …

(t .. c - t).any((d) => c % d < o)); } } The : range operator needs an Integer (the number of elements) as a second argument, so we use the .. operator, which takes the same type as the first argument …

i * 2^k ].fold(0)((y, z) => y.xor(z))) i }.empty).take(n); This creates an infinite iterable of integers (starting with 2), filters it by checking if a number …

any((d) => c%d < 1) ) // then take the first n elements .take(n) // print each element .each(print); This uses the same basic prime check as my answer to the "Is this number …

Ceylon, 86 bytes Object m(Integer+l)=>let(c=l.paired.map(([x,y])=>x<=>y))[if(!smaller in c)equal in c]; The function takes the input as its parameters, and returns a tuple of zero or one booleans – …

Ceylon, 98 bytes import ceylon.whole{l=one}Integer q(Integer n)=>sum({0,*product({l,*(l:n)}).string*.offset('0')}); Try it online Explanation: This is quite long, because we need to convince th …