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

1,3

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

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 *)

Prog

(PARI) mono(n)=n=eval(Vec(Str(n))); for(i=2, #n, if(n[i]<n[i-1], return(0))); 1
for(n=1, 1e5, if(mono(n^2), print1(n", "))) \\ 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

Crossrefs

Cf. A000290, A028820.

Sequence in context: A032342 A023762 A032903 * A234841 A353725 A108948

Adjacent sequences: A028816 A028817 A028818 * A028820 A028821 A028822

Keyword

nonn,base

Author

Patrick De Geest

Status

approved