A256065 Zeroless numbers that when incremented or decremented by the product of their digits produce a square.

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

Offset

1,1

Comments

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.

Intersection of A066567, A228187, and A052382.

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.

a(80) > 10^27. - Hiroaki Yamanouchi, Mar 16 2015

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..79

Example

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.

Prog

(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, ", ")))

Crossrefs

Cf. A066567 (when incremented), A228187 (when decremented), A052382 (zeroless).

Sequence in context: A046967 A007753 A272331 * A081979 A012672 A024340

Adjacent sequences: A256062 A256063 A256064 * A256066 A256067 A256068

Keyword

nonn,base

Author

Derek Orr, Mar 13 2015

Extensions

a(12)-a(19) from Michel Marcus, Mar 14 2015

a(20)-a(25) from Hiroaki Yamanouchi, Mar 16 2015

Status

approved