OFFSET
1,1
COMMENTS
Conjecture: (1) Sequence is infinite. (2) For every prime signature there corresponds a term in this sequence.
From Robert Israel, Jul 02 2024: (Start)
Conjecture (2) is false: k and its 10's complement can't both have prime signature p^m where m is even.
If k is a term, then so is 10 * k.
It appears that the first term with m prime factors, counted with multiplicity, is 3 * 10^((m-1)/2) if m is odd and 132 * 10^((m-4)/2) if m >= 4 is even. (End)
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
EXAMPLE
35 is a member as 35= 5*7 and its 10's complement (100-35) = 65 = 13*5 both have the prime signature p*q.
35 is a member as 35 = 5*7 and its 10's complement (100-35) = 65 = 13*5 both have the prime signature p*q.
MAPLE
ps:= n -> sort(ifactors(n)[2][.., 2]):
tc:= n -> 10^(1+ilog10(n))-n:
select(n -> ps(n) = ps(tc(n)), [$1..1000]); # Robert Israel, Jul 02 2024
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Sep 04 2003
EXTENSIONS
More terms from David Wasserman, May 06 2005
STATUS
approved