A119509 Positive numbers whose square contains no digit more than once.

1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 16, 17, 18, 19, 23, 24, 25, 27, 28, 29, 31, 32, 33, 36, 37, 42, 43, 44, 48, 49, 51, 52, 53, 54, 55, 57, 59, 61, 64, 66, 69, 71, 72, 73, 74, 78, 79, 82, 84, 86, 87, 89, 93, 95, 96, 98, 99, 113, 116, 117, 118, 124, 126, 128, 133

Offset: 1

Author

Tanya Khovanova, Jul 26 2006

Keywords

• base
• fini
• full
• nonn

Comments

There are exactly 610 terms. a(610) = 99066 and 99066^2 = 9814072356. - Rick L. Shepherd, Jul 27 2006

If we count 0, there is one more term, for a total of 611. - T. D. Noe, Jun 21 2013

Links

• Rick L. Shepherd, Table of n, a(n) for n = 1..610 (full sequence)

Crossrefs

Subsequence of A045540 = numbers whose squares contain an equal number of each digit that they contain. The first number that belongs to A045540 and doesn't belong to this sequence is number 88.

Cf. A078255, A036745, A075309, A162950.

Programs

Magma

[n: n in [1..10^5] | #Set(d) eq #d where d is Intseq(n^2)];  // Bruno Berselli, Aug 02 2011

Maple

lim:=floor(sqrt(9876543210)): A119509:={}: for n from 1 to lim do pandig:=true: d:=convert(n^2,base,10): for k from 0 to 9 do if(numboccur(k, d)>1)then pandig:=false: break: fi: od: if(pandig)then A119509 := A119509 union {n}: fi: od: op(sort(convert(A119509,list))); # Nathaniel Johnston, Jun 23 2011

Mathematica

Select[Range[1000000], Length[IntegerDigits[ # ^2]] == Length[Union[IntegerDigits[ # ^2]]] &] (* Tanya Khovanova, May 29 2007 *)
Select[Range[10^5], Max[DigitCount[#^2]] <= 1 &] (* T. D. Noe, Aug 02 2011 *)

PARI

is_A119509(n)=#(n=digits(n^2))==#Set(n) \\ M. F. Hasler, Sep 08 2017

Python

def ok(n): s = str(n**2); return n > 0 and len(set(s)) == len(s)
afull = [k for k in range(10**5) if ok(k)] # Michael S. Branicky, Nov 27 2022

Extensions

More terms from Rick L. Shepherd, Jul 27 2006