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A378498 Squares where larger digits have smaller multiplicity.

%I A378498 #18 Nov 29 2024 21:04:23
%S A378498 1,4,9,100,121,225,400,484,676,900,10000,11881,40000,44944,69696,
%T A378498 90000,111556,202500,220900,225625,232324,261121,265225,300304,442225,
%U A378498 444889,695556,1000000,1002001,1020100,1210000,2250000,2295225,4000000,4008004,4080400,4840000,5112121,6760000,8008900,9000000
%N A378498 Squares where larger digits have smaller multiplicity.
%C A378498 Conjecture: a(n) ≍ n^2. - _Charles R Greathouse IV_, Nov 29 2024
%H A378498 Charles R Greathouse IV, <a href="/A378498/b378498.txt">Table of n, a(n) for n = 1..10000</a>
%F A378498 n^2 << a(n) << 1.001^n. - _Charles R Greathouse IV_, Nov 29 2024
%t A378498 decreasingQ[L_]:=Max[Rest[(L-RotateRight[L])]]<0;
%t A378498 sortedQ[n_]:=decreasingQ[Sort[Tally[IntegerDigits[n]]][[All,2]]];
%t A378498 Select[Range[10000]^2, sortedQ]
%o A378498 (PARI) has(n)=my(d=matreduce(digits(n))[,2]); for(i=2,#d, if(d[i]>=d[i-1], return(0))); 1
%o A378498 list(lim)=my(v=List()); for(n=1,sqrtint(lim\1), if(has(n^2), listput(v,n^2))); Vec(v) \\ _Charles R Greathouse IV_, Nov 29 2024
%Y A378498 Cf. A000290, A018884, A052046, A235718, A378492.
%K A378498 nonn,base
%O A378498 1,2
%A A378498 _Erich Friedman_, Nov 28 2024