[seqfan] Re: Is Primes in A061909 (skinny numbers which are primes) identical to A085306?

franktaw at netscape.net franktaw at netscape.net
Sat Mar 20 02:10:27 CET 2010

Let's back off and look at the underlying sequences.

I think A085305 (numbers such that the reversal of their square is 
equal to the square of their reversal) is wrong; it should be a 
duplicate of A061909.  E.g., the reversal of 10 is 1, 1^2 = 1; 10^2 = 
100, and the reversal of 100 is also 1.  It appears that multiples of 
10 were arbitrarily excluded from A085305.

I can't actually prove that these sequences are the same, but they seem 
to be.  (The binary equivalents are not the same, since 3 = 11_2 and 
3^2 = 1001_2 are both palindromes.  Of course, skinny numbers in base 2 
are only the powers of 2.)  There are a couple of comments in A061909 
and a program which assume that the skinny numbers are the numbers 
having the reversal property specified in A085305, but no flat 
statement that these are the same.

Naturally, if these sequences are the same, the primes in them are the 

Franklin T. Adams-Watters

P.S. A061909 contains a comment reading in part "... if there is a 3 
then there can be no 2's. If there are any 2's then there can be no 
3's."  The latter sentence is redundant.

-----Original Message-----
From: Jonathan Post <jvospost3 at gmail.com>

Is Primes in A061909 (skinny numbers which are primes):
2, 3, 11, 13, 31, 101, 103, 113, 211, 311, 1013, 1021, 1031, 1103, 1201
identical to A085306    Prime numbers such that first reversing digits
and after squaring equals the result of first-squaring and
after-reversing. identical to A085306.
or, if not, where do they diverge?

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