A028819 Numbers whose square has its digits in nondecreasing order.

0, 1, 2, 3, 4, 5, 6, 7, 12, 13, 15, 16, 17, 34, 35, 37, 38, 67, 83, 106, 107, 116, 117, 167, 183, 334, 335, 337, 367, 383, 587, 667, 1633, 1667, 3334, 3335, 3337, 3367, 3383, 3667, 4833, 6667, 16667, 33334, 33335, 33337, 33367, 33667, 36667, 66667

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

It appears that from a(53) onwards all terms have nondecreasing digits and has one of the following forms: 16..67, 3..34, 3..35, 3..37, 3..367, 3..36..67, 36..67 and 6..67 and all number of such forms are terms. - Chai Wah Wu, Dec 07 2015

Links

• Charles R Greathouse IV and Chai Wah Wu, Table of n, a(n) for n = 1..422 (n = 1..107 from Charles R Greathouse IV).
• Patrick De Geest, Palindromic Squares in bases 2 to 17

Crossrefs

Cf. A000290, A028820.

Programs

Mathematica

okQ[n_]:=And@@(#[[2]]>=#[[1]]&/@Partition[IntegerDigits[n^2],2,1])
Select[Range[0,50000],okQ]  (* Harvey P. Dale, Jan 09 2011 *)
Select[Range[0,10^5],LessEqual@@IntegerDigits[#^2]&] (* Ray Chandler, Jan 06 2014 *)

PARI

mono(n)=n=eval(Vec(Str(n)));for(i=2,#n,if(n[i]Charles R Greathouse IV, Aug 22 2011

Python

from itertools import combinations_with_replacement
from gmpy2 import is_square, isqrt
A028819_list = [0] + [int(isqrt(n)) for n in (int(''.join(i)) for l in range(1,11) for i in combinations_with_replacement('123456789',l)) if is_square(n)] # Chai Wah Wu, Dec 07 2015