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- #!/usr/bin/ruby
- # Least number k such that k^n and k^n-1 contain the same number of prime factors (counted with multiplicity) or 0 if no such k exists.
- # https://oeis.org/A241793
- # Known terms:
- # 3, 34, 5, 15, 17, 55, 79, 5, 53, 23, 337, 13, 601, 79, 241, 41, 18433, 31, 40961, 89, 3313, 1153
- # Lower-bounds:
- # a(23) > 170369
- include("../../../factordb/auto.sf")
- func a(m, from=2) {
- for k in (from..Inf) {
- var n = bigomega(k)*m
- var v = (k**m - 1)
- say "[#{k}] Checking: #{v}"
- if (k.is_prime && (v.len > 60)) {
- say ":: Checking factordb..."
- var f = try { FF_factordb(v) }
- if (defined(f)) {
- say ":: Success..."
- if (f.len == n) {
- return k
- }
- else {
- next
- }
- }
- else {
- say ":: Fail..."
- }
- }
- v.is_almost_prime(n) || next
- return k
- }
- }
- var from = 157668
- for n in (23) {
- say "a(#{n}) = #{a(n, from)}"
- }
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