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A031149
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Numbers n such that n^2 with last digit deleted is still a perfect square.
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18
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0, 1, 2, 3, 4, 7, 13, 16, 19, 38, 57, 136, 253, 487, 604, 721, 1442, 2163, 5164, 9607, 18493, 22936, 27379, 54758, 82137, 196096, 364813, 702247, 870964, 1039681, 2079362, 3119043, 7446484, 13853287, 26666893, 33073696, 39480499, 78960998, 118441497, 282770296
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Square root of A023110(n).
For the first 4 terms, the square has only one digit, but in analogy to the sequences in other bases (A204502, A204512, A204514, A204516, A204518, A204520, A004275, A055793, A055792), it is understood that deleting this digit yields 0.
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REFERENCES
| R. K. Guy, Neg and Reg, preprint, Jan 2012. [From N. J. A. Sloane, Jan 12 2012]
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FORMULA
| Appears to satisfy: a(n)=38a(n-7)-a(n-14) which would require a(-k) to look like 3, 2, 1, 4, 7, 13, 16, 57, 38, 19, 136, ... for k>0. - Henry Bottomley (se16(AT)btinternet.com), May 08 2001
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EXAMPLE
| 364813^2 = 133088524969, 115364^2 = 13308852496
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MAPLE
| for i from 1 to 150000 do if (floor(sqrt(10 * i^2 + 9)) > floor(sqrt(10 * i^2))) then print(floor(sqrt(10 * i^2 + 9))) end if end do;
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MATHEMATICA
| fQ[n_] := IntegerQ@ Sqrt@ Quotient[n^2, 10]; Select[ Range[ 0, 40000000], fQ] (* From Harvey P. Dale, June 15 2011 *) (modified by Robert G. Wilson v, Jan 16 2012 *)
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CROSSREFS
| Cf. A023110, A030686, A030687, A031150.
Sequence in context: A057983 A200088 A004783 * A096723 A137495 A099779
Adjacent sequences: A031146 A031147 A031148 * A031150 A031151 A031152
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KEYWORD
| nonn,base
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AUTHOR
| Patrick De Geest (pdg(AT)worldofnumbers.com)
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EXTENSIONS
| Added 4 initial terms. M. F. Hasler, Jan 15 2012
a(40) from Robert G. Wilson v, Jan 15 2012
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