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

1,2

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

Formula

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A069707 A129967 A182020 * A087553 A061850 A061459

Adjacent sequences: A378495 A378496 A378497 * A378499 A378500 A378501

Keyword

nonn,base

Author

Erich Friedman, Nov 28 2024

Status

approved