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A256065
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Zeroless numbers that when incremented or decremented by the product of their digits produce a square.
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1
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2, 8, 46692, 58896, 59949, 186633, 186673, 949968, 1587616, 2989584, 58988961, 245878784, 914457625, 2439577764, 2754991369, 4161798288, 4161798468, 4629457984, 4897936656, 29859851664, 34828536976, 41664977536, 59998484736, 96745892625, 134994579556
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OFFSET
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1,1
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COMMENTS
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If a term has a zero in it, its digit product is 0. Thus it is trivial to include cubes with one or more zeros.
Is this sequence finite?
Replacing "squares" with "cubes", this sequence would only consist of {4} for n < 10^8. 4 is believed to be the only number to satisfy this property with cubes.
If it exists, a(20) > 10^10.
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LINKS
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EXAMPLE
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46692 + 4*6*6*9*2 = 49284 = 222^2 and 46692 - 4*6*6*9*2 = 210^2. So 46692 is a member of this sequence.
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PROG
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(PARI) for(n=0, 10^7, d=digits(n); p=prod(i=1, #d, d[i]); if(p&&issquare(n-p)&&issquare(n+p), print1(n, ", ")))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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