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 1-6 of 6 results.

A294664 Numbers n such that the largest digit of n^3 is 4.

Original entry on oeis.org

7, 68, 70, 324, 680, 700, 3240, 6800, 7000, 7618, 31177, 32400, 52308, 68000, 69314, 70000, 76180, 311770, 324000, 353068, 523080, 680000, 693140, 700000, 756658, 761800, 1039247, 2715974, 2732441, 3117700, 3240000, 3511617, 3530680, 4689368, 5230800, 6800000, 6931400, 7000000
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Comments

For any term a(n), all numbers of the form a(n)*10^k, k >= 0, are in this sequence. Primitive terms, i.e., not of this form (or equivalently: without trailing '0'), are 7, 68, 324, 7618, 31177, 52308, 69314, 353068, 756658, 1039247, 2715974, 2732441, 3511617, 4689368, 7571814, 12811968, 15904541, ...
All terms have last nonzero digit 1, 4, 7 or 8 and leading digit <= 7. - Robert Israel, Nov 13 2017
The number formed by the first m digits of a term is always less than c*10^m with c = (4/9)^(1/3) = .7631428283688879... - M. F. Hasler, Nov 13 2017

Examples

			7 is in the sequence because the largest digit of 7^3 = 343 is 4.

Crossrefs

Cf. A294663 (the corresponding cubes), A278937, A294665, A294996 - A294999 (analog for digits 3, 5, 6 - 9); A277961 (analog for squares).
Cf. A000578 (the cubes).

Programs

  • Maple
    select(n -> max(convert(n^3,base,10))=4, [$1..10^6]); # Robert Israel, Nov 13 2017
  • PARI
    for(n=1,2e8, vecmax(digits(n^3))==4&&print1(n","))

A295021 Cubes whose largest digit is 6.

Original entry on oeis.org

64, 216, 15625, 46656, 50653, 64000, 132651, 216000, 262144, 456533, 614125, 636056, 1601613, 1643032, 2406104, 2515456, 3112136, 3652264, 6331625, 10360232, 13144256, 15625000, 41063625, 46656000, 50653000, 52313624, 55306341, 56623104, 64000000, 66430125, 100544625
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

			64 is in the sequence because it is a cube, 64 = 4^3, and its largest digit is 6.

Crossrefs

Cf. A294996 (the corresponding cube roots); A278936, A294663, A295025, A295022, A295023, A295024 (same for digit 3 .. 9); A295016 (same for squares).
Cf. A000578 (the cubes).

Programs

  • Mathematica
    Select[Range[500]^3,Max[IntegerDigits[#]]==6&] (* Harvey P. Dale, Jun 21 2022 *)
  • PARI
    for(n=1,500, vecmax(digits(n^3))==6 &&print1(n^3,","))

Formula

a(n) = A294996(n)^3.

A294999 Numbers n such that the largest digit of n^3 is 9.

Original entry on oeis.org

9, 13, 16, 17, 19, 21, 27, 28, 29, 31, 33, 34, 39, 41, 43, 45, 46, 48, 49, 57, 58, 59, 61, 66, 69, 71, 73, 76, 79, 84, 89, 90, 97, 98, 99, 103, 106, 108, 109, 112, 113, 116, 119, 124, 125, 128, 129, 130, 131, 132, 139, 143, 144, 148, 149, 151, 156, 157, 158, 159, 160, 164, 165, 166, 169
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^k, k >= 0, are in this sequence. We could call "primitive" the terms not of this form, i.e., without trailing '0'.

Examples

			13 is in the sequence because the largest digit of 13^3 = 2197 is 9.

Crossrefs

Cf. A295024 (the corresponding cubes); A278937, A294664, A294665, A294996, A294997, A294998 (same for digit 3, ..., 8).
Cf. A000578 (the cubes).

Programs

  • Mathematica
    Select[Range[200],Max[IntegerDigits[#^3]]==9&] (* Harvey P. Dale, Jul 08 2018 *)
  • PARI
    for(n=1,200, vecmax(digits(n^3))==9&&print1(n","))

A295006 Numbers n such that the largest digit of n^2 is 6.

Original entry on oeis.org

4, 6, 8, 16, 19, 25, 34, 40, 46, 51, 56, 58, 60, 66, 68, 75, 79, 80, 81, 106, 108, 116, 119, 121, 125, 129, 142, 146, 156, 160, 162, 175, 190, 204, 206, 208, 215, 216, 225, 231, 238, 245, 246, 248, 249, 250, 251, 252, 254, 255, 256, 258, 325, 334, 340, 354, 355, 369, 375, 379
Offset: 1

Views

Author

M. F. Hasler, Nov 12 2017

Keywords

Examples

			19 is in this sequence because 19^2 = 361 has 6 as largest digit.

Links

Crossrefs

Cf. A295016 (the corresponding squares), A277959, A277960, A277961, A295005 .. A295009 (analog for digits 2 through 9), A294996 (analog for cubes).
Cf. A000290 (the squares).

Programs

  • Mathematica
    Select[Range[400],Max[IntegerDigits[#^2]]==6&] (* Harvey P. Dale, Mar 30 2024 *)
  • PARI
    select( is_A295006(n)=n&&vecmax(digits(n^2))==6 , [0..999]) \\ The "n&&" avoids an error message for n=0.

Formula

a(n) = sqrt(A295016(n)), where sqrt = A000196 or A000194 or A003059.

A294997 Numbers n such that the largest digit of n^3 is 7.

Original entry on oeis.org

3, 14, 15, 23, 26, 30, 54, 55, 56, 63, 65, 67, 78, 91, 105, 111, 121, 126, 133, 135, 137, 140, 147, 150, 163, 167, 168, 173, 176, 188, 197, 226, 230, 245, 256, 258, 260, 273, 276, 291, 293, 295, 300, 318, 321, 343, 346, 375, 376, 385, 386, 397, 415, 417, 418, 424, 425, 488, 497
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^k, k >= 0, are in this sequence. We could call "primitive" the terms not of this form, i.e., without trailing '0'.

Examples

			3 is in the sequence because the largest digit of 3^3 = 27 is 7.

Crossrefs

Cf. A295022 (the corresponding cubes); A278937, A294664, A294665, A294996 .. A294999 (same for digit 3, ..., 9).
Cf. A000578 (the cubes).

Programs

  • Mathematica
    Select[Range[500],Max[IntegerDigits[#^3]]==7&] (* Harvey P. Dale, Sep 10 2019 *)
  • PARI
    for(n=1,2e3, vecmax(digits(n^3))==7&&print1(n","))

A294998 Numbers n such that the largest digit of n^3 is 8.

Original entry on oeis.org

2, 12, 18, 20, 22, 24, 32, 35, 38, 42, 44, 47, 52, 53, 62, 72, 75, 82, 83, 87, 88, 92, 93, 94, 95, 96, 102, 104, 114, 115, 120, 122, 123, 127, 138, 141, 142, 145, 152, 153, 155, 161, 162, 172, 174, 180, 182, 183, 186, 192, 194, 195, 200, 201, 202, 203, 205, 206, 217, 220, 228, 232, 238, 240, 242, 244, 251
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^k, k >= 0, are in this sequence. We could call "primitive" the terms not of this form, i.e., without trailing '0'.

Examples

			12 is in the sequence because the largest digit of 12^3 = 1728 is 8.

Links

Crossrefs

Cf. A295023 (the corresponding cubes); A278937, A294664, A294665, A294996 .. A294999 (same for digit 3, ..., 9); A295008 (same for squares).
Cf. A000578 (the cubes).

Programs

  • Maple
    filter:= n -> max(convert(n^3,base,10))=8:
select(filter, [$1..1000]); # Robert Israel, Jul 03 2020
  • Mathematica
    Select[Range[300],Max[IntegerDigits[#^3]]==8&] (* Harvey P. Dale, Aug 21 2019 *)
  • PARI
    for(n=1,500, vecmax(digits(n^3))==8&&print1(n","))
Showing 1-6 of 6 results.

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

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