cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A295019 Squares whose largest digit is 9.

Original entry on oeis.org

9, 49, 169, 196, 289, 529, 729, 900, 961, 1089, 1296, 1369, 1849, 1936, 2209, 2809, 2916, 3249, 3969, 4096, 4489, 4900, 5329, 5929, 6889, 7396, 7569, 7921, 8649, 9025, 9216, 9409, 9604, 9801, 10609, 11449, 12769, 12996, 13689, 13924, 15129, 16129, 16900, 17689, 17956, 18496, 18769
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Crossrefs

Cf. A295009 (square roots of the terms), A277946 - A277948 (same for digit 2..4), A295015 - A295018 (same for digit 5..8).
Cf. A000290 (the squares).

Programs

  • Mathematica
    Select[Range[150]^2,Max[IntegerDigits[#]]==9&] (* Harvey P. Dale, Oct 27 2019 *)
  • PARI
    is_A295019(n)=issquare(n)&&n&&vecmax(digits(n))==9 \\ "&&n" avoids an error message for n=0.

Formula

a(n) = A295009(n)^2.

A295008 Numbers whose square has largest digit 8.

Original entry on oeis.org

9, 22, 28, 29, 41, 59, 62, 72, 78, 90, 91, 92, 94, 104, 109, 122, 126, 128, 135, 151, 159, 168, 169, 178, 184, 191, 192, 195, 196, 202, 209, 220, 221, 232, 241, 242, 259, 261, 262, 268, 278, 279, 280, 284, 285, 289, 290, 291, 292, 294, 295, 296, 298, 322, 328, 329, 341, 344, 349
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Comments

Includes a*10^n+b for n >= 2 and [a,b] in {[4, 1], [9, 1], [2, 2], [9, 2], [1, 4], [6, 4], [9, 4], [8, 5], [4, 6], [9, 6], [5, 8], [8, 8], [9, 8], [1, 9], [2, 9], [4, 9], [6, 9], [8, 9], [9, 9]}. - Robert Israel, Nov 13 2017

Examples

			28 is in this sequence because 28^2 = 784 has 8 as largest digit.

Links

Crossrefs

Cf. A295018 (the corresponding squares), A277959 .. A277961 (same for digit 2 .. 4), A295005 .. A295009 (same for digit 5 .. 9).
Cf. A000290 (the squares).

Programs

  • Maple
    select(t -> max(convert(t^2,base,10))=8, [$1..1000]); # Robert Israel, Nov 13 2017
  • Mathematica
    Select[Range[400],Max[IntegerDigits[#^2]]==8&] (* Harvey P. Dale, Jun 02 2019 *)
  • PARI
    select( is_A295008(n)=n&&vecmax(digits(n^2))==8 , [0..999]) \\ The "n&&" avoids an error message for n=0.
  • Python
    def ok(n): return max(int(d) for d in str(n*n)) == 8
print(list(filter(ok, range(350)))) # Michael S. Branicky, Sep 22 2021

Formula

a(n) = sqrt(A295018(n)), where sqrt = A000196 or A000194 or A003059.

A295023 Cubes whose largest digit is 8.

Original entry on oeis.org

8, 1728, 5832, 8000, 10648, 13824, 32768, 42875, 54872, 74088, 85184, 103823, 140608, 148877, 238328, 373248, 421875, 551368, 571787, 658503, 681472, 778688, 804357, 830584, 857375, 884736, 1061208, 1124864, 1481544, 1520875, 1728000, 1815848, 1860867, 2048383, 2628072, 2803221
Offset: 1

Views

Author

M. F. Hasler, Nov 13 2017

Keywords

Comments

For any term a(n), all numbers of the form a(n)*10^3k, k >= 0, are in this sequence. We could call "primitive" the terms not of this form, i.e., those without trailing '0'.

Examples

			8 is in the sequence because it is a cube, 8 = 2^3, and its largest digit is 8.

Crossrefs

Cf. A294998 (the corresponding cube roots), A278936, A294663, A295025, A295021, A295022, A295024 (same for digit 3 .. 9), A295018 (same for squares).
Cf. A000578 (the cubes).

Programs

  • PARI
    for(n=1,200, vecmax(digits(n^3))==8 &&print1(n^3,","))

Formula

a(n) = A294998(n)^3.
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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