A294665 -id:A294665 - cp's OEIS frontend

A294996 Numbers n such that the largest digit of n^3 is 6.

4, 6, 25, 36, 37, 40, 51, 60, 64, 77, 85, 86, 117, 118, 134, 136, 146, 154, 185, 218, 236, 250, 345, 360, 370, 374, 381, 384, 400, 405, 465, 510, 585, 586, 587, 600, 606, 625, 640, 705, 770, 805, 806, 825, 845, 850, 860, 1011, 1021, 1045, 1046, 1081, 1101, 1124, 1136, 1145, 1146, 1170, 1177, 1180

Offset: 1

M. F. Hasler, Nov 13 2017

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'.

Includes a*10^k+b for k >= 3 and [a,b] in {[11, 1], [5, 4], [4, 5], [6, 5], [5, 6], [11, 10], [1, 11], [10, 11]}, and 8*10^k+8 for k >= 4. - Robert Israel, Jul 22 2019

			4 is in the sequence because the largest digit of 4^3 = 64 is 6.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A295021 (the corresponding cubes); A278937, A294664, A294665, A294997 .. A294999 (same for digit 3, ..., 9); A295006 (same for squares).

Cf. A000578 (the cubes).

for(n=1,2e3, vecmax(digits(n^3))==6&&print1(n","))

A295025 Cubes whose largest digit is 5.

Original entry on oeis.org

125, 512, 125000, 405224, 512000, 531441, 1225043, 5000211, 5545233, 13312053, 43243551, 54010152, 102503232, 115501303, 125000000, 221445125, 320013504, 400315553, 405224000, 512000000, 531441000, 1204550144, 1225043000, 2053225511, 2253243231, 2543302125

Offset: 1

M. F. Hasler, Nov 12 2017

For any term a(n), all numbers of the form a(n)*10^3k, k >= 0, are in this sequence. Primitive terms, i.e., not of this form (or equivalently: without trailing '0'), are 125, 512, 405224, 531441, 1225043, 5000211, 5545233, 13312053, 43243551, ...

			512 is in the sequence because it is a cube, 512 = 8^3, and its largest digit is 5.

Cf. A294665 (the corresponding cube roots), A278936 and A294663 (same for digit 3 and 4).

Cf. A000578 (the cubes).

for(n=1,2e8, vecmax(digits(n^3))==5&&print1(n^3,","))

def ok(cube): return max(str(cube)) == "5"
print([c for c in (i**3 for i in range(1370)) if ok(c)]) # Michael S. Branicky, Dec 05 2021

a(n) = A294665(n)^3.

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

M. F. Hasler, Nov 12 2017

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

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

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

Cf. A000578 (the cubes).

select(n -> max(convert(n^3,base,10))=4, [$1..10^6]); # Robert Israel, Nov 13 2017

for(n=1,2e8, vecmax(digits(n^3))==4&&print1(n","))

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

M. F. Hasler, Nov 13 2017

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'.

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

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

Cf. A000578 (the cubes).

Select[Range[200],Max[IntegerDigits[#^3]]==9&] (* Harvey P. Dale, Jul 08 2018 *)

for(n=1,200, vecmax(digits(n^3))==9&&print1(n","))

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

M. F. Hasler, Nov 13 2017

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'.

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

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

Cf. A000578 (the cubes).

Select[Range[500],Max[IntegerDigits[#^3]]==7&] (* Harvey P. Dale, Sep 10 2019 *)

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

M. F. Hasler, Nov 13 2017

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'.

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

Cf. A000578 (the cubes).

filter:= n -> max(convert(n^3,base,10))=8:
select(filter, [$1..1000]); # Robert Israel, Jul 03 2020

Select[Range[300],Max[IntegerDigits[#^3]]==8&] (* Harvey P. Dale, Aug 21 2019 *)

for(n=1,500, vecmax(digits(n^3))==8&&print1(n","))

cp's OEIS Frontend

A294996 Numbers n such that the largest digit of n^3 is 6.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

A295025 Cubes whose largest digit is 5.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

PARI

Python

Formula

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Maple

PARI

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

PARI

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI