A028820 Squares with digits in nondecreasing order.

0, 1, 4, 9, 16, 25, 36, 49, 144, 169, 225, 256, 289, 1156, 1225, 1369, 1444, 4489, 6889, 11236, 11449, 13456, 13689, 27889, 33489, 111556, 112225, 113569, 134689, 146689, 344569, 444889, 2666689, 2778889, 11115556, 11122225, 11135569

Offset: 1

Author

Patrick De Geest

Keywords

• nonn
• base

Comments

Number of terms less than 10^k, beginning with k=0: 1, 4, 8, 13, 19, 25, 32, 34, 42, 43, 50, 53, 61, 62, 71, 72, 82, 83, 94, 95, …, .

Like all squares the ending digits can be 0, 1, 4, 5, 6 or 9. Here is the tally of the list of terms < 10^19: {0, 1}, {1, 1}, {4, 4}, {5, 10}, {6, 13}, {9, 66}. Robert G. Wilson v, Jan 01 2014

Links

• Robert G. Wilson v and Chai Wah Wu, Table of n, a(n) for n = 1..428 (n = 1..106 from Robert G. Wilson v).
• Patrick De Geest, Palindromic Squares in bases 2 to 17

Crossrefs

Cf. A028819, A028821, A028822, A237424.

Intersection of A000290 and A009994.

Programs

Mathematica

Select[Range[0,4000]^2,Min[Differences[IntegerDigits[#]]]>-1&] (* Harvey P. Dale, Dec 31 2013 *)
Select[Range[0,10^4]^2,LessEqual@@IntegerDigits[#]&] (* 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
A028820_list = [0] + [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

Formula

a(n) = A028819(n)^2. - Ray Chandler, Jan 06 2014

Extensions

Definition edited by Zak Seidov, Dec 31 2013