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A028819 Numbers n such that n^2 has digits in nondecreasing order. 4
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 (list; graph; refs; listen; history; text; internal format)
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).

P. 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. A028820.

Sequence in context: A032342 A023762 A032903 * A234841 A108948 A107818

Adjacent sequences:  A028816 A028817 A028818 * A028820 A028821 A028822

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

STATUS

approved

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Last modified September 16 09:08 EDT 2019. Contains 327093 sequences. (Running on oeis4.)