prog.sf

#!/usr/bin/ruby

# Index of smallest Fibonacci number with n prime factors when counted with multiplicity.
# https://oeis.org/A072396

# Known terms:
#   3, 8, 6, 20, 18, 12, 30, 54, 24, 36, 138, 48, 84, 72, 108, 96, 210, 120, 276, 168, 216, 252, 288, 240, 336, 570, 384, 420, 360, 576, 480, 540, 504, 660, 600, 672, 990, 720, 792, 840, 1152, 1140

# Lower-bounds:
#   a(43) > 1452

# 1452 < a(43) <= 1596. a(44) = 1296. a(45) = 1368. a(46) = 1080. a(47) = 1200. a(48) <= 1728.

include("../../../factordb/auto.sf")

func a(n, from=1) {
    for k in (from..Inf) {
        #k.is_prime && next
        var t = fib(k)
        say "[#{n},#{k}] Checking: #{t}"
        if (try { bigomega(t) == n } catch { t.is_almost_prime(n) }) {
        #if (t.is_almost_prime(n)) {
            return k
        }
    }
}

say a(48)

#~ for n in (1..100) {
    #~ say "a(#{n}) = #{a(n)}"
#~ }