A028820 - OEIS

%I #38 Feb 10 2025 20:04:00

%S 0,1,4,9,16,25,36,49,144,169,225,256,289,1156,1225,1369,1444,4489,

%T 6889,11236,11449,13456,13689,27889,33489,111556,112225,113569,134689,

%U 146689,344569,444889,2666689,2778889,11115556,11122225,11135569

%N Squares with digits in nondecreasing order.

%C 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, …, .

%C 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

%H Robert G. Wilson v and Chai Wah Wu, <a href="/A028820/b028820.txt">Table of n, a(n) for n = 1..428</a> (n = 1..106 from Robert G. Wilson v).

%H Patrick De Geest, <a href="https://www.worldofnumbers.com/nobase10pg2.htm">Palindromic Squares in bases 2 to 17</a>

%F a(n) = A028819(n)^2. - _Ray Chandler_, Jan 06 2014

%t Select[Range[0,4000]^2,Min[Differences[IntegerDigits[#]]]>-1&] (* _Harvey P. Dale_, Dec 31 2013 *)

%t Select[Range[0,10^4]^2,LessEqual@@IntegerDigits[#]&] (* _Ray Chandler_, Jan 06 2014 *)

%o (PARI) mono(n)=n=eval(Vec(Str(n)));for(i=2,#n,if(n[i]<n[i-1],return(0)));1

%o for(n=1,800,if(mono(n^2),print1(n^2", "))) \\ _Charles R Greathouse IV_, Aug 22 2011

%o (Python)

%o from itertools import combinations_with_replacement

%o from gmpy2 import is_square

%o 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

%Y Cf. A028819, A028821, A028822, A237424.

%Y Intersection of A000290 and A009994.

%K nonn,base

%O 1,3

%A _Patrick De Geest_

%E Definition edited by _Zak Seidov_, Dec 31 2013