A052046 -id:A052046 - cp's OEIS frontend

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

Erich Friedman, Nov 28 2024

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

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

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

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

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

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

A078256 Triangular numbers in which frequency of occurrence of every digit is same.

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 190, 210, 231, 253, 276, 325, 351, 378, 406, 435, 465, 496, 528, 561, 630, 666, 703, 741, 780, 820, 861, 903, 946, 1035, 1275, 1326, 1378, 1485, 1540, 1596, 1653, 1830, 1953, 2016, 2145

Offset: 1

Amarnath Murthy, Nov 24 2002

Andrew Howroyd, Table of n, a(n) for n = 1..10000

Cf. A052046, A082646.

T[n_] := n*(n + 1)/2;f[n_] := Block[{dc = DigitCount[n], s},s = Select[dc, Positive];Min @@ s == Max @@ s];Select[Array[T, 70, 0], f] (* Ray Chandler, May 11 2007 *)

\\ here isok(k) tests if each digit k has equal frequency.
isok(k)={my(f=vector(10)); foreach(digits(k), t, f[1+t]++); my(c=vecmax(f)); 0==#select(t->t>0&&tAndrew Howroyd, Sep 21 2024

Offset changed by Andrew Howroyd, Sep 21 2024

cp's OEIS Frontend

A378498 Squares where larger digits have smaller multiplicity.

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