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

1,2

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)

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 *)

Prog

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

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.

Sequence in context: A135140 A052061 A045540 * A219248 A055568 A360822

Adjacent sequences: A119506 A119507 A119508 * A119510 A119511 A119512

Keyword

base,fini,full,nonn

Author

Tanya Khovanova, Jul 26 2006

Extensions

More terms from Rick L. Shepherd, Jul 27 2006

Status

approved