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%I #20 Aug 11 2024 14:41:29
%S 0,1,4,9,64,81,100,400,441,841,900,961,6400,7744,8100,10000,40000,
%T 44100,84100,90000,96100,640000,774400,810000,1000000,4000000,4410000,
%U 8410000,8874441,9000000,9610000,9853321,64000000,77440000
%N Squares with digits in nonincreasing order.
%C From _Robert G. Wilson v_, Jan 02 2014: (Start)
%C If x is present so is 100x. The primitives are 0, 1, 4, 9, 64, 81, 441, 841, 961, 7744, 8874441, 9853321, 999887641, …, . = A062826. Their square roots are: 0, 1, 2, 3, 8, 9, 21, 29, 31, 88, 2979, 3139, 31621, …, . Are there no more primitives?
%C Number of terms less than 10^k, beginning with k=0: 1, 4, 6, 12, 15, 21, 24, 32, 35, 44, 47, 56, 59, 68, 71, 80, 83, 92, 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 < 10^18: {0, 84}, {1, 8}, {4, 3}, {5, 0}, {6, 0}, {9, 1}. (End)
%H Robert G. Wilson v, <a href="/A028822/b028822.txt">Table of n, a(n) for n = 1..96</a>
%H P. De Geest, <a href="https://www.worldofnumbers.com/square.htm">Palindromic Squares</a>
%F For n > 1, a(n) = A062826(i) * 10^j for some i and j. - _Charles R Greathouse IV_, Jan 02 2014
%F a(n) = A028821(n)^2. - _Ray Chandler_, Jan 05 2014
%t fQ[n_] := Max[ Differences[ IntegerDigits[ n]]] < 1; Select[ Range[0, 9000]^2, fQ] (* _Robert G. Wilson v_, Jan 02 2014 *)
%t Select[Range[0,10^4]^2,GreaterEqual@@IntegerDigits[#]&] (* _Ray Chandler_, Jan 05 2014 *)
%o (PARI) isA009996(n)=n=digits(n); for(i=2,#n,if(n[i]>n[i-1],return(0))); 1
%o is(n)=issquare(n) && isA009996(n) \\ _Charles R Greathouse IV_, Jan 02 2014
%Y Cf. A062826, A028820, A028821, A009996.
%K nonn,base
%O 1,3
%A _Patrick De Geest_
%E Better name from _Robert G. Wilson v_, Jan 02 2014
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