

A132660


Numbers which, together with their squares in base ten, contain all digits from 1 to 9 exactly twice.


0



339542, 355877, 372554, 385263, 388943, 415683, 423413, 435267, 487386, 513728, 514377, 538271, 578979, 625958, 629721, 657971, 661977, 731618, 738792, 739278, 753921, 797454, 853892, 856529, 963458
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OFFSET

1,1


COMMENTS

Also of note is the unique number 314, which together with its sixth power 958468597212736 has the property that each digit from 1 to 9 occurs exactly twice. Aside from trivial cases that use zeroth powers, these are all the cases where two numbers that are powers of the same base have this property. [Comment corrected by Tanya Khovanova, Dec 18 2007]
Found by exhaustive search.


LINKS

Table of n, a(n) for n=1..25.


EXAMPLE

355877^2 = 126648439129.


MATHEMATICA

Select[Range[1000000], Sort[Join[IntegerDigits[ # ], IntegerDigits[ #^2 ]]] == {1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 8, 8, 9, 9} & ]  Tanya Khovanova, Dec 18 2007


CROSSREFS

Sequence in context: A224632 A350186 A234726 * A236609 A103808 A251996
Adjacent sequences: A132657 A132658 A132659 * A132661 A132662 A132663


KEYWORD

base,fini,full,nonn


AUTHOR

WeiHwa Huang (onigame(AT)gmail.com), Nov 15 2007


EXTENSIONS

Many terms were wrong. Corrected by Zak Seidov, Nov 19 2007


STATUS

approved



