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A066567 Numbers that when incremented by the product of their digits produce a square. 4
2, 8, 13, 63, 91, 100, 128, 185, 215, 221, 337, 400, 448, 456, 549, 551, 559, 681, 900, 1024, 1089, 1151, 1185, 1215, 1221, 1327, 1348, 1437, 1600, 1651, 1897, 2025, 2112, 2191, 2196, 2209, 2293, 2304, 2392, 2401, 2448, 2500, 2539, 2544, 2551, 2596, 2601 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

EXAMPLE

63 belongs to this sequence as 63 + 6*3 = 81 = 9^2.

MATHEMATICA

f[n_] := n + Apply[ Times, IntegerDigits[n]]; Select[ Range[ 2500], IntegerQ[ Sqrt[ f[ # ]]] & ]

PROG

(PARI) ProdD(x)= { local(p=1); while (x>9 && p>0, p*=x%10; x\=10); return(p*x) } { n=0; for (m=1, 10^10, if (issquare(m + ProdD(m)), write("b066567.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Mar 05 2010

CROSSREFS

Cf. A066564.

Sequence in context: A257036 A077241 A228469 * A002248 A194278 A050619

Adjacent sequences:  A066564 A066565 A066566 * A066568 A066569 A066570

KEYWORD

base,nonn

AUTHOR

Amarnath Murthy, Dec 18 2001

EXTENSIONS

More terms from Robert G. Wilson v, Dec 22 2001

Offset changed from 0 to 1 by Harry J. Smith, Mar 05 2010

STATUS

approved

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Last modified August 20 03:34 EDT 2017. Contains 290823 sequences.