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A028820 Squares with digits in nondecreasing order. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

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).

P. De Geest, Palindromic Squares

FORMULA

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

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 *)

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, 800, if(mono(n^2), print1(n^2", "))) \\ 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

CROSSREFS

Cf. A028819, A028821, A028822, A237424.

Sequence in context: A122541 A133743 A235484 * A122683 A235597 A309002

Adjacent sequences:  A028817 A028818 A028819 * A028821 A028822 A028823

KEYWORD

nonn,base

AUTHOR

Patrick De Geest

EXTENSIONS

Definition edited by Zak Seidov, Dec 31 2013

STATUS

approved

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Last modified August 6 18:25 EDT 2020. Contains 336256 sequences. (Running on oeis4.)