f:*:    / first
r:{y!x} / residue

/ previous 1
f'-1_{(x!1_)\!y}[2]5    / josephus
({~x!2}(_.5*)/1+3*)\27  / syracuse

/ previous 2
5(|+\)\1 1      / fibonacci
f(|r\)\24 40        / euclid

/ previous all
5{x,+/-2#x}/1

/ previous with global
5{+[Y::x]Y}\Y::1