A278936 -id:A278936 - cp's OEIS frontend

A278937 Numbers k such that 3 is the largest decimal digit of k^3.

11, 101, 110, 1001, 1010, 1100, 10001, 10010, 10100, 11000, 100001, 100010, 100100, 101000, 110000, 684917, 1000001, 1000010, 1000100, 1001000, 1010000, 1100000, 6849170, 10000001, 10000010, 10000100, 10001000, 10010000, 10100000, 11000000

Offset: 1

Colin Barker, Dec 02 2016

A038444 is a subsequence. Are there an infinite number of terms not in A038444 that are not a multiple of 10? - Chai Wah Wu, Dec 02 2016
Conjecture: sequence is equal to A038444 plus terms of the form 684917*10^k for k >= 0. - Chai Wah Wu, Sep 02 2017
Conjecture is true up to 4.8*10^18. - Giovanni Resta, Sep 03 2017

			684917 is in the sequence because 684917^3 = 321302302131323213.

Chai Wah Wu, Table of n, a(n) for n = 1..130

Cf. A000578 (the cubes: n^3), A038444, A277960 (analog for squares), A278936 (cubes of the terms: a(n)^3).

Cf. A031997 (the odd terms).

[n: n in [1..2*10^7] | Max(Intseq(n^3)) eq 3]; // Vincenzo Librandi, Dec 03 2016

Select[Range[11 10^6],Max[IntegerDigits[#^3]]==3&] (* Harvey P. Dale, Feb 11 2025 *)

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

a(n)^3 = A278936(n).

A294663 Cubes whose largest digit is 4.

Original entry on oeis.org

343, 314432, 343000, 34012224, 314432000, 343000000, 34012224000, 314432000000, 343000000000, 442102433032, 30304210142233, 34012224000000, 143121324002112, 314432000000000, 333014302331144, 343000000000000, 442102433032000, 30304210142233000, 34012224000000000

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 343, 314432, 34012224, 442102433032, 30304210142233, 143121324002112, 333014302331144, ...

			343 is in the sequence because it is a cube, 343 = 7^3, and its largest digit is 4.

Cf. A294664 (the corresponding cubic roots).
Cf. A277948 = A277961^2 (analog for squares).
Cf. A278936, A295025, A295021, ..., A295024 (analog for digits 3, 5, 6, ..., 9).
Cf. A000578 (the cubes).

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

a(n) = A294664(n)^3.

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.

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

M. F. Hasler, Nov 13 2017

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'.

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

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).

Select[Range[500]^3,Max[IntegerDigits[#]]==6&] (* Harvey P. Dale, Jun 21 2022 *)

for(n=1,500, vecmax(digits(n^3))==6 &&print1(n^3,","))

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

A295022 Cubes whose largest digit is 7.

Original entry on oeis.org

27, 2744, 3375, 12167, 17576, 27000, 157464, 166375, 175616, 250047, 274625, 300763, 474552, 753571, 1157625, 1367631, 1771561, 2000376, 2352637, 2460375, 2571353, 2744000, 3176523, 3375000, 4330747, 4657463, 4741632, 5177717, 5451776, 6644672, 7645373, 11543176, 12167000

Offset: 1

M. F. Hasler, Nov 13 2017

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'.

			27 is in the sequence because it is a cube, 27 = 3^3, and its largest digit is 7.

Cf. A294997 (the corresponding cube roots); A278936, A294663, A295025, A295021, A295023, A295024 (same for digit 3 .. 9); A295017 (same for squares).

Cf. A000578 (the cubes).

for(n=1,250, vecmax(digits(n^3))==7 &&print1(n^3,","))

a(n) = A294997(n)^3.

A295024 Cubes whose largest digit is 9.

Original entry on oeis.org

729, 2197, 4096, 4913, 6859, 9261, 19683, 21952, 24389, 29791, 35937, 39304, 59319, 68921, 79507, 91125, 97336, 110592, 117649, 185193, 195112, 205379, 226981, 287496, 328509, 357911, 389017, 438976, 493039, 592704, 704969, 729000, 912673, 941192, 970299, 1092727, 1191016

Offset: 1

M. F. Hasler, Nov 13 2017

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'.

			2197 is in the sequence because it is a cube, 2197 = 13^3, and its largest digit is 9.

Cf. A294999 (the corresponding cube roots), A278936, A294663, A295025, A295021, A295022, A295023 (same for digit 3 .. 8), A295019 (same for squares).

Cf. A000578 (the cubes).

for(n=1,150, vecmax(digits(n^3))==8 &&print1(n^3,","))

a(n) = A294999(n)^3.

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

M. F. Hasler, Nov 13 2017

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'.

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

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).

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

a(n) = A294998(n)^3.

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

cp's OEIS Frontend

A278937 Numbers k such that 3 is the largest decimal digit of k^3.

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A294663 Cubes whose largest digit is 4.

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A295025 Cubes whose largest digit is 5.

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A295021 Cubes whose largest digit is 6.

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A295022 Cubes whose largest digit is 7.

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A295024 Cubes whose largest digit is 9.

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A295023 Cubes whose largest digit is 8.

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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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