A294663 -id:A294663 - cp's OEIS frontend

A295025 Cubes whose largest digit is 5.

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","))

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.

A294662 Least k > a(n-1) such that k^3 has no digit in common with a(n-1) and a(n+1), a(0)=0.

Original entry on oeis.org

0, 1, 2, 4, 5, 6, 7, 8, 9, 10, 29, 55, 88, 90, 111, 200, 211, 400, 518, 654, 888, 889, 1111, 2825, 3131, 4244, 11111, 28222, 31535, 42449, 53355, 90000, 111181, 590000, 618181, 900000, 1111115, 9000000, 11111115, 60660090, 114144155

Offset: 0

M. F. Hasler, Nov 09 2017

This is the sequence which corresponds to the original definition of A030290, before it was corrected to reproduce the data (and the intended meaning).

			a(3) cannot be 3 because 3^3 = 27 would have the digit '2' in common with a(2) = 2, therefore a(3) = 4, which does not violate this condition.
After a(9) = 10, none of the numbers { 11, ..., 19 } can follow, because they have the digit '1' in common with a(9)^3 = 1000. Numbers { 20, ..., 28 } are excluded because their cube would have a digit '0' or '1' in common with a(9). Therefore, a(10) = 29 which hasn't a digit in common with a(9)^3, nor has 29^3 = 24389 a digit in common with a(9).
a(38) = 11111115 with 11111115^3 = 1371743552812575445875 using all digits except for 0, 6 and 9. So a(39) = 60660090 is possible, with a(39)^3 = 223207688999086038729000 having all digits except for 1, 4 and 5.

Cf. A030290, A294663.

nxt(a,L=oo,D(a)=Set(digits(a)),S=D(a),T=D(a^3))={for(k=a+1,L, #setintersect(D(k),T)||#setintersect(D(k^3),S)||return(k))}
A294662=List(); a=0; until(!a=nxt(a,1e7),write("/tmp/A294662.txt",#A294662," ",a);listput(A294662,a))

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A295025 Cubes whose largest digit is 5.

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

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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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A294662 Least k > a(n-1) such that k^3 has no digit in common with a(n-1) and a(n+1), a(0)=0.

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