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Numbers k such that k and k^2 use only the digits 0, 1, 3, 5 and 8.
2

%I #17 Apr 12 2024 09:51:26

%S 0,1,10,100,1000,10000,58151,100000,550501,581510,1000000,5505010,

%T 5815100,5818151,10000000,55050100,55055001,58151000,58181510,

%U 100000000,183031501,550501000,550550010,555005001,581510000,581815100,1000000000,1000550501,1005055001,1830315010,3180155001,3318358151,5505010000,5505500100,5505550001

%N Numbers k such that k and k^2 use only the digits 0, 1, 3, 5 and 8.

%C Generated with DrScheme.

%H Jonathan Wellons and Chai Wah Wu, <a href="/A136845/b136845.txt">Table of n, a(n) for n = 1..237</a> (first 174 terms from Jonathan Wellons).

%H J. Wellons, <a href="https://web.archive.org/web/20090206165028/http://jonathanwellons.com/shared-digits/">Tables of Shared Digits</a> [archived]

%e 58151^2 = 3381538801.

%e 581858058583151^2 = 338558800338153581101581088801.

%o (Python)

%o from itertools import product

%o A136845_list = [0,1]

%o for l in range(15):

%o ....for a in ('1','3','5','8'):

%o ........for b in product('01358',repeat=l):

%o ............for c in ('0','1','5'):

%o ................n = int(''.join([a]+list(b)+[c]))

%o ................if set(str(n*n)) <= {'0','1','3','5','8'}:

%o ....................A136845_list.append(n) # _Chai Wah Wu_, May 25 2015

%K base,nonn

%O 1,3

%A Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008