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A054038 Numbers n such that n^2 contains every digit at least once. 28
32043, 32286, 33144, 35172, 35337, 35757, 35853, 37176, 37905, 38772, 39147, 39336, 40545, 42744, 43902, 44016, 45567, 45624, 46587, 48852, 49314, 49353, 50706, 53976, 54918, 55446, 55524, 55581, 55626, 56532, 57321, 58413, 58455 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are 87 terms < 10^5; these are the n such that n^2 uses each digit exactly once. - David Wasserman, Feb 03 2005

The squares in this sequence are in A190682. - Bruno Berselli, May 23 2011

REFERENCES

J.-M. De Koninck and A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 239 pp. 39; 178, Ellipses Paris 2004.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 4866 terms from Klaus Brockhaus)

MAPLE

f := []; for i from 0 to 200 do if nops({op(convert(i^2, base, 10))})=10 then f := [op(f), i] fi; od; f;

MATHEMATICA

A050278 = Select[FromDigits@#&/@Permutations[Range[0, 9], {10}], # > 10^9 &]; Sqrt[Select[A050278, IntegerQ[Sqrt[#]] &]] (* Alonso del Arte, Jun 18 2011, based on a program by Robert G. Wilson v *)

Select[Sqrt[#]&/@FromDigits/@Select[Permutations[Range[0, 9]], #[[1]]>0&], IntegerQ] (* Harvey P. Dale, May 26 2016 *)

PROG

(MAGMA) IsA054038:=func< n | Seqset(Intseq(n^2)) eq {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} >; [ n: n in [1..60000] | IsA054038(n) ]; // Klaus Brockhaus, May 16 2011

(PARI) is(n)=#vecsort(Vec(Str(n^2)), , 8)==10 \\ Charles R Greathouse IV, Jun 18 2011

CROSSREFS

Cf. A016069, A054031, A054032, A054033, A054034, A054035, A054036, A054037, A054039.

Sequence in context: A197114 A224621 A231613 * A156977 A217368 A097282

Adjacent sequences:  A054035 A054036 A054037 * A054039 A054040 A054041

KEYWORD

nonn,base

AUTHOR

Asher Auel (asher.auel(AT)reed.edu), Feb 28 2000

EXTENSIONS

More terms from David Wasserman, Feb 03 2005

STATUS

approved

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Last modified May 31 00:53 EDT 2020. Contains 334747 sequences. (Running on oeis4.)