A278937 -id:A278937 - cp's OEIS frontend

A278936 Cubes whose largest decimal digit is 3.

1331, 1030301, 1331000, 1003003001, 1030301000, 1331000000, 1000300030001, 1003003001000, 1030301000000, 1331000000000, 1000030000300001, 1000300030001000, 1003003001000000, 1030301000000000, 1331000000000000, 321302302131323213, 1000003000003000001

Offset: 1

Colin Barker, Dec 02 2016

			321302302131323213 is in the sequence because 321302302131323213 = 684917^3 and its largest digit is 3.

Cf. A000578, A277947 (same for squares), A278937 (the cube roots).

[n^3: n in [1..2*10^7] | Max(Intseq(n^3)) eq 3]; // Bruno Berselli, Dec 02 2016

Select[Range[1000010]^3,Max[IntegerDigits[#]]==3&] (* Harvey P. Dale, Feb 09 2019 *)

select(n->vecmax(digits(n))==3, vector(1000000, n, n^3))

a(n) = A278937(n)^3.

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

Original entry on oeis.org

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","))

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","))

A294665 Numbers n such that the largest digit of n^3 is 5.

Original entry on oeis.org

5, 8, 50, 74, 80, 81, 107, 171, 177, 237, 351, 378, 468, 487, 500, 605, 684, 737, 740, 800, 810, 1064, 1070, 1271, 1311, 1365, 1474, 1605, 1645, 1710, 1724, 1758, 1770, 2247, 2364, 2370, 2474, 2485, 2824, 2885, 2925, 3247, 3510, 3780, 4680, 4718, 4870, 4934, 5000, 5247

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 5, 8, 74, 81, 107, 171, 177, 237, 351, 378, 468, 487, 605, 684, 737, 1064, 1271, 1311, 1365, 1474, 1605, 1645, 1724, 1758, ...

			8 is in the sequence because the largest digit of 8^3 = 512 is 5.

Cf. A295025 (the corresponding cubes), A278937 and A294664 (same for digit 3 and 4).

Cf. A000578 (the cubes).

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

A031997 Odd numbers which when cubed give number composed just of the digits 0, 1, 2, 3.

Original entry on oeis.org

1, 11, 101, 1001, 10001, 100001, 684917, 1000001, 10000001, 100000001, 1000000001, 10000000001, 100000000001, 1000000000001, 10000000000001, 100000000000001, 1000000000000001, 10000000000000001, 100000000000000001, 1000000000000000001

Offset: 1

Robert G. Wilson v, Jun 23 2001

Note that 684917 (whose cube is 321302302131323213) so far is the only entry not of the form 10^x + 1.

Cf. A030175, A043681, A278936, A278937.

Do[ If[ Union[ IntegerDigits[ n^3 ] ] [ [ -1 ] ] < 4, Print[ n ] ], {n, 1, 10^9, 2} ] (* corrected by Friedjof Tellkamp, Apr 24 2025 *)
(* faster code *)
DigitsLEQ3[n_] := And @@ (LessEqual[#, 3] & /@ IntegerDigits[n])
Arr = {1, 7}; For[i = 1, i < 10, i++, Arr = Flatten[Table[Select[Arr + 10^i j, DigitsLEQ3[Mod[#^3, 10^(i+1)]] &], {j, 0, 9}]]];
Select[Arr, DigitsLEQ3[#^3] &] (* Friedjof Tellkamp, Apr 25 2025 *)

A031997_list = [n for n in range(1,10**6,2) if max(str(n**3)) <= '3'] # Chai Wah Wu, Feb 23 2016

Term 0 removed and a(12)-a(17) added by Chai Wah Wu, Feb 25 2016

a(18)-a(20) from Giovanni Resta, Mar 14 2020

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

A278936 Cubes whose largest decimal digit is 3.

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

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

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A294665 Numbers n such that the largest digit of n^3 is 5.

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

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A031997 Odd numbers which when cubed give number composed just of the digits 0, 1, 2, 3.

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

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

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