login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 2
1, 1, 2, 3, 23, 3 (list; graph; refs; listen; history; text; internal format)
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.

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: A137077 A046965 A119679 * 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 21 11:11 EST 2020. Contains 331105 sequences. (Running on oeis4.)