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A156977 Numbers n such that n^2 contains every decimal digit exactly once. 10
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, 58554, 59403, 60984 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

There are exactly 87 such numbers, no one of them being prime.

Since 0 + 1 +...+ 9 = 5*9, every pandigital number is divisible by 9, hence no a(n) can be prime. - Giovanni Resta, Mar 19 2013

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..87 (full sequence)

FORMULA

a(n) = sqrt(A036745(n)).

MAPLE

lim:=floor(sqrt(9876543210)): for n from floor(sqrt(1023456789)) to lim do d:=[op(convert(n^2, base, 10))]: pandig:=true: for k from 0 to 9 do if(numboccur(k, d)<>1)then pandig:=false: break: fi: od: if(pandig)then printf("%d, ", n): fi: od: # Nathaniel Johnston, Jun 22 2011

MATHEMATICA

Select[Range[Floor@Sqrt@1023456789, Ceiling@Sqrt@9876543210], Sort@IntegerDigits[#^2] == Range[0, 9] &] (* Giovanni Resta, Mar 19 2013 *)

PROG

(MAGMA) [n: n in [Floor(Sqrt(1023456789))..Ceiling(Sqrt(9876543210))] | Set(Intseq(n^2)) eq {0..9}]; // Bruno Berselli, Mar 19 2013 (after Giovanni Resta)

CROSSREFS

Cf. A036745, A054037, A054038.

Sequence in context: A224621 A231613 A054038 * A217368 A097282 A264499

Adjacent sequences:  A156974 A156975 A156976 * A156978 A156979 A156980

KEYWORD

fini,full,nonn,base

AUTHOR

Zak Seidov, Feb 20 2009

STATUS

approved

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Last modified February 26 12:33 EST 2020. Contains 332279 sequences. (Running on oeis4.)