

A174397


Sum of any three adjacent digits of n^2 is a square.


0



10, 11, 12, 13, 14, 15, 18, 20, 21, 22, 23, 30, 31, 90, 100, 200, 263, 265, 300, 900, 985, 1000, 1002, 2000, 2001, 3000, 5265, 9000, 10000, 10002, 10020, 20000, 20001, 20010, 30000, 90000, 100000, 100002, 100020, 100200, 200000, 200001, 200010, 200100, 262987, 300000, 900000, 1000000, 1000002, 1000020, 1000200, 1002000, 2000000, 2000001, 2000010, 2000100, 2001000, 2001002, 3000000
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OFFSET

1,1


LINKS

Table of n, a(n) for n=1..59.


EXAMPLE

262987^2=69162162169 and 6+9+1=16, 9+1+6=16, 1+6+2=9, 6+2+1=9, 2+1+6=9, 1+6+2=9, 6+2+1=9, 2+1+6=9, 1+6+9=16 are all squares.


MATHEMATICA

s={}; Do[id=IntegerDigits[n^2];
If[Union[IntegerQ/@(Sqrt[Total/@Partition[id, 3, 1]])]=={True}, Print[n]; AppendTo[s, n]], {n, 10, 3*10^6}]
Select[Range[10, 3*10^6], AllTrue[Total/@Partition[IntegerDigits[#^2], 3, 1], IntegerQ[ Sqrt[#]]&]&] (* Harvey P. Dale, Jan 21 2019 *)


CROSSREFS

Cf.A061910 Numbers n such that sum of digits of n^2 is a square.
Sequence in context: A008710 A058946 A118379 * A297266 A296707 A297140
Adjacent sequences: A174394 A174395 A174396 * A174398 A174399 A174400


KEYWORD

nonn,base


AUTHOR

Zak Seidov, Nov 28 2010


STATUS

approved



