A087324 -id:A087324 - cp's OEIS frontend

A087325 Numbers k such that k and its 10's complement both have the same prime signature.

3, 5, 7, 11, 14, 15, 17, 26, 29, 30, 35, 38, 41, 47, 50, 53, 59, 62, 65, 70, 71, 74, 83, 85, 86, 89, 94, 97, 110, 111, 113, 122, 129, 132, 134, 137, 140, 150, 153, 158, 170, 173, 174, 179, 183, 185, 186, 187, 191, 195, 201, 206, 209, 212, 215, 219, 221, 227, 236

Offset: 1

Amarnath Murthy, Sep 04 2003

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)

			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.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A087324, A089186. Contains A068811.

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

More terms from David Wasserman, May 06 2005

cp's OEIS Frontend

A087325 Numbers k such that k and its 10's complement both have the same prime signature.

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