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A077439 Numbers n such that n and n^2 have square decimal digits. 3
0, 1, 10, 100, 1000, 1049, 10000, 10490, 100000, 100499, 104900, 1000000, 1004990, 1049000, 10000000, 10004999, 10049900, 10490000, 100000000, 100049990, 100499000, 104900000, 1000000000, 1000049999, 1000499900, 1004990000, 1044049999, 1049000000, 10000000000, 10000499990, 10004999000, 10049900000, 10440499990 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers n such that n and the square of n use only the digits 0, 1, 4 and 9.

Notice the trick used in the first Mathematica program to convert decimal numbers to base 4 numbers and then map threes into nines and then twos into fours. This saves a lot of computing. - Robert G. Wilson v, Nov 08 2002

LINKS

Jonathan Wellons, Table of n, a(n) for n=1..68

J. Wellons, Tables of Shared Digits

EXAMPLE

1049^2 = 1100401, therefore 1049 is a term; whereas A046030(6)=14 is not a term, as 14^2=196 and 6 is not a square digit.

104900499999000^2 = 11004114900040199000001000000

MATHEMATICA

a = {}; Do[d = FromDigits[ ReplaceAll[ IntegerDigits[n, 4], {3 -> 9, 2 -> 4}]]; If[ Union[ Join[ IntegerDigits[d^2], {0, 1, 4, 9}]] == {0, 1, 4, 9}, a = Append[a, d]], {n, 0, 3*10^5}]; a

With[{c={0, 1, 4, 9}}, Select[FromDigits/@Tuples[c, 11], SubsetQ[c, IntegerDigits[ #^2]]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jan 15 2017 *)

CROSSREFS

A077440(n) = a(n)^2.

Cf. A046030, A019544, A000290.

Sequence in context: A115814 A171758 A115798 * A136839 A136863 A031201

Adjacent sequences:  A077436 A077437 A077438 * A077440 A077441 A077442

KEYWORD

base,nonn

AUTHOR

Reinhard Zumkeller, Nov 06 2002

EXTENSIONS

Edited by Robert G. Wilson v, Nov 08 2002

More terms from Jonathan Wellons (wellons(AT)gmail.com), Jan 22 2008

Edited by N. J. A. Sloane, May 15 2008 at the suggestion of R. J. Mathar.

STATUS

approved

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Last modified June 5 18:48 EDT 2020. Contains 334854 sequences. (Running on oeis4.)