A046827 Numbers k such that k^2 contains all the digits of k with the same or higher multiplicity.

0, 1, 5, 6, 10, 11, 25, 27, 50, 60, 63, 64, 74, 76, 95, 96, 100, 101, 105, 110, 125, 139, 142, 205, 250, 255, 261, 270, 275, 277, 278, 285, 305, 364, 371, 376, 405, 421, 441, 463, 472, 493, 497, 500, 501, 502, 503, 504, 505, 506, 507, 508, 509, 523, 524, 525

Offset: 1

Author

David W. Wilson

Keywords

• nonn
• base

Comments

10^n is a term for all n. - Amarnath Murthy, Aug 03 2005

Examples

			27 is a term as 27^2 = 729 contains 2 and 7.
255 is a term as 255^2 = 65025 which contains the digits 2,5,5. 502 is a term as 502^2 = 252004 which contains 5, 0, 2.
		

Crossrefs

Cf. A046829, A029772.

Cf. A064827 (essentially the same).

Programs

Maple

isA046827 := proc(n) local dgsn,dgsnsq,multsn,multsn2,o,i ;
dgsn := sort(convert(n,base,10)) ;
dgsnsq := sort(convert(n^2,base,10)) ;
multsn := [seq(0,i=0..9) ] ;
multsn2 := [seq(0,i=0..9) ] ; for i from 1 to nops(dgsn) do o := op(1+op(i,dgsn),multsn) ; multsn := subsop( 1+op(i,dgsn)=o+1,multsn ) ; od: for i from 1 to nops(dgsnsq) do o := op(1+op(i,dgsnsq),multsn2) ; multsn2 := subsop( 1+op(i,dgsnsq)=o+1,multsn2 ) ; od: for i from 1 to 10 do if op(i,multsn2) < op(i,multsn) then RETURN(false) ; fi ; od: RETURN(true) ; end: for n from 1 to 700 do if isA046827(n) then printf("%d,",n) ; fi ; od; # R. J. Mathar, Feb 11 2008

Mathematica

Join[{0}, Select[Range[525], Count[Table[DigitCount[#^2, 10, k] - DigitCount[#, 10, k], {k, Union[IntegerDigits[#]]}], ?Negative] == 0 &]] (* _Jayanta Basu, Jun 29 2013 *)

Python

from itertools import count, islice
from collections import Counter
def A046827_gen(startvalue=0): # generator of terms >= startvalue
    return filter(lambda k:Counter(str(k))<=Counter(str(k**2)),count(max(startvalue,0)))
A046827_list = list(islice(A046827_gen(),20)) # Chai Wah Wu, Apr 03 2023

Extensions

Edited by N. J. A. Sloane, Aug 23 2008 at the suggestion of R. J. Mathar