A132660 Numbers which, together with their squares in base ten, contain all digits from 1 to 9 exactly twice.

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

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

Wei-Hwa Huang (onigame(AT)gmail.com), Nov 15 2007

Extensions

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

Status

approved