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

1,3

Comments

Similar to A120716, which uses the proper divisors of n. Other known values include a(10) = 347, a(14) = 349, and a(16) = 311. See also A191859.

Links

Table of n, a(n) for n=1..6.

Example

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

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

Crossrefs

Cf. A130846, A066272, A120716, A191647.

Sequence in context: A046965 A119679 A361669 * A130846 A114101 A114007

Adjacent sequences: A191645 A191646 A191647 * A191649 A191650 A191651

Keyword

nonn,base,more,hard

Author

Paolo P. Lava, Jun 10 2011

Status

approved