sub-unit_squares.sf

#!/usr/bin/ruby

# Efficient algorithm for generating sub-unit squares.

# A sub-unit square is a square number that remains a square after having a 1 subtracted from each digit in the square.

# See also:
#   https://oeis.org/A061844
#   https://rosettacode.org/wiki/Sub-unit_squares

local Num!USE_FACTORDB = true

func difference_of_two_squares(n) {     # x solutions to n = x^2 - y^2
    divisors(n, n.isqrt).map {|d|

        var a = d
        var b = n/d

        (a+b).is_even || next

        (a + b)>>1
    }.flip
}

var N   = 20      # how many terms to compute
var arr = Set(1)

var index = 1
say (index, ' ', 1)

for n in (1..Inf) {
    var r = (10**n - 1)/9

    var new = difference_of_two_squares(r).grep {|k|
        var d = k.sqr.digits
        (d[-1] != 1) && d.none{.is_zero} && d.map{.dec}.digits2num.is_square
    }.map{.sqr}

    new.each {|v|
        next if arr.has(v)
        say (++index, ' ', v)
        arr << v
    }

    break if (arr.len >= N)
}