A090515 Duplicate of A075309.
1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 125, 128, 169, 196, 216, 243, 256, 289, 324
Offset: 1
This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
100116^2 = 10023213456 is a term because it has 11 digits, ceiling(11/10) = 2 and no digit occurs more than twice. This is the first term after 9814072356.
Select[Range[0,80]^2,Max[DigitCount[#]]==1&] (* The program only selects numbers with no more than 10 digits, and even that would require changing the high Range constant to 100000. *) (* Harvey P. Dale, Sep 06 2020 *)
from itertools import count, islice def c(n): return all((s:=str(n)).count(d)<=(len(s)-1)//10+1 for d in "0123456789") def agen(): yield from filter(c, (k*k for k in count(0))) print(list(islice(agen(), 50))) # Michael S. Branicky, Oct 29 2023
[n: n in [1..10^5] | #Set(d) eq #d where d is Intseq(n^2)]; // Bruno Berselli, Aug 02 2011
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
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 *)
is_A119509(n)=#(n=digits(n^2))==#Set(n) \\ M. F. Hasler, Sep 08 2017
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
N:= 5000:
filter:= proc(n) local L;
L:= convert(n,base,10);
not member(0, L[2..-1]-L[1..-2])
end proc:
P:= sort(convert({seq(seq(i^k,i=1..floor(N^(1/k))),k=2..ilog2(N))},list)):
select(filter, P); # Robert Israel, Sep 03 2018
The 8 powers with unique digits in base 5 are 1, 4, 8, 9, 16, 27, 144, and 576; in base 5 these are 1, 4, 13, 14, 31, 102, 1304, and 4301.
okdigs(digs) = {for (i = 1, #digs-1, for (j = i+1, #digs, if (digs[j] == digs[i], return (0);););); return (1);}
a(n) = {b = n; sols = Set([1]); vmax = b^b; pmax = ceil(log(vmax)/log(2)); for (p = 2, pmax, i = 2; while ((iep = i^p) < vmax, if (okdigs(digits(iep, b)), sols = Set(concat(sols, iep));); i++;);); #sols;} \\ Michel Marcus, Aug 19 2013
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