A191648 a(1)=1, a(2)=1. For n > 2, start with n and iterate the map (k -> concatenation of anti-divisors of k) until we reach a prime q; then a(n) = q. If we never reach a prime, a(n) = 0.
1, 1, 2, 3, 23, 3
Offset: 1
Examples
The anti-divisors of 5 are 2, 3, and 23 is prime, hence a(5) = 23. The anti-divisors of 7 are 2, 3, 5, and 235 is composite; the anti-divisors of 235 are 2, 3, 7, 10, 67, 94, 157, and 237106794157 = 59*547*7346909 is composite; the anti-divisors of 237106794157 start 2, 3, 5, 15, 118, 1094, 1709, 4519, 61403, 64546, 7722971, 14693818, 104937727, but the others are unknown, hence a(7) is also unknown. Note that the example speaks of the anti-divisors of 237106794157 being incomplete. As of this date, those are well-established (see code of A066272). It is the primality evaluation chain from anti-divisors for n=7 from 23515118109417094519614036454677229711469381810493772727748015786693526280375184463161423922194842717663158071196105 that is incomplete. - _Bill McEachen_, Dec 14 2022
Programs
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Maple
antidivisors := proc(n) local a, k; a := {} ; for k from 2 to n-1 do if abs((n mod k)- k/2) < 1 then a := a union {k} ; end if; end do: a ; end proc: A130846 := proc(n) digcatL(sort(convert(antidivisors(n),list))) ; end proc: A191648 := proc(n) if n <=2 then 1; else m := A130846(n) ; while not isprime(m) do m := A130846(m) ; end do: return m; end if; end proc: # R. J. Mathar, Jun 30 2011
Comments