A378498 Squares where larger digits have smaller multiplicity.

1, 4, 9, 100, 121, 225, 400, 484, 676, 900, 10000, 11881, 40000, 44944, 69696, 90000, 111556, 202500, 220900, 225625, 232324, 261121, 265225, 300304, 442225, 444889, 695556, 1000000, 1002001, 1020100, 1210000, 2250000, 2295225, 4000000, 4008004, 4080400, 4840000, 5112121, 6760000, 8008900, 9000000

Offset: 1

Author

Erich Friedman, Nov 28 2024

Keywords

• nonn
• base

Comments

Conjecture: a(n) ≍ n^2. - Charles R Greathouse IV, Nov 29 2024

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000290, A018884, A052046, A235718, A378492.

Programs

Mathematica

decreasingQ[L_]:=Max[Rest[(L-RotateRight[L])]]<0;
sortedQ[n_]:=decreasingQ[Sort[Tally[IntegerDigits[n]]][[All,2]]];
Select[Range[10000]^2, sortedQ]

PARI

has(n)=my(d=matreduce(digits(n))[,2]); for(i=2,#d, if(d[i]>=d[i-1], return(0))); 1
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

Formula

n^2 << a(n) << 1.001^n. - Charles R Greathouse IV, Nov 29 2024