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: A378493 A378494 A378495 * A378500 A378503 A378504

Keyword

nonn,base

Author

Erich Friedman, Nov 28 2024

Status

approved