A291644 -id:A291644 - cp's OEIS frontend

A291639 Numbers k such that 0 is the smallest decimal digit of k^3.

10, 16, 20, 22, 30, 34, 37, 40, 42, 43, 47, 48, 50, 52, 59, 60, 63, 67, 69, 70, 73, 74, 79, 80, 84, 86, 87, 89, 90, 93, 94, 99, 100, 101, 102, 103, 106, 107, 109, 110, 112, 115, 116, 117, 118, 120, 123, 124, 126, 127, 128, 130, 131, 134, 135, 138, 140, 141

Offset: 1

Colin Barker, Aug 28 2017

The sequence is infinite. For example, A062397(i) is in the sequence for any i > 1, since A168575(i) contains the digit 0 for any i > 1. - Felix Fröhlich, Aug 28 2017

Also contains A008592, and has asymptotic density 1. - Robert Israel, Aug 29 2017

			16 is in the sequence because 16^3 = 4096, the smallest decimal digit of which is 0.

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

Cf. A008592, A062397, A168575, A291640, A291641, A291642, A291643, A291644.

select(n -> min(convert(n^3,base,10))=0, [$1..1000]); # Robert Israel, Aug 29 2017

Select[Range[150],DigitCount[#^3,10,0]>0&] (* Harvey P. Dale, Feb 03 2025 *)

select(k->vecmin(digits(k^3))==0, vector(500, k, k))

A291642 Numbers k such that 3 is the smallest decimal digit of k^3.

Original entry on oeis.org

7, 15, 33, 46, 76, 77, 95, 96, 157, 167, 175, 179, 186, 197, 207, 213, 215, 326, 327, 332, 335, 353, 355, 379, 389, 427, 429, 437, 454, 457, 464, 714, 764, 775, 813, 816, 826, 859, 883, 922, 927, 942, 957, 1526, 1529, 1553, 1557, 1636, 1692, 1695, 1753, 1782

Offset: 1

Colin Barker, Aug 28 2017

			33 is in the sequence because 33^3 = 35937, the smallest decimal digit of which is 3.

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

Cf. A291639, A291640, A291641, A291643, A291644.

filter:= n -> min(convert(n^3,base,10))=3:
select(filter, [$1..10000]); # Robert Israel, Aug 29 2017

Select[Range[2000],Min[IntegerDigits[#^3]]==3&] (* Harvey P. Dale, Aug 31 2025 *)

select(k->vecmin(digits(k^3))==3, vector(5000, k, k))

A291643 Numbers k such that 4 is the smallest decimal digit of k^3.

Original entry on oeis.org

4, 36, 204, 786, 842, 1682, 2114, 3795, 3859, 3863, 4429, 4459, 4559, 4635, 7644, 7913, 7914, 8183, 8286, 8372, 8744, 8864, 9144, 9263, 9599, 16592, 17094, 17863, 18923, 19035, 19563, 19829, 20364, 20635, 20776, 36264, 38183, 38389, 38432, 40186, 44216

Offset: 1

Colin Barker, Aug 28 2017

			4 is in the sequence because 4^3 = 64, the smallest decimal digit of which is 4.

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Cf. A291639, A291640, A291641, A291642, A291644.

Select[Range[50000],Min[IntegerDigits[#^3]]==4&] (* Harvey P. Dale, Aug 13 2019 *)

select(k->vecmin(digits(k^3))==4, vector(50000, k, k))

A291640 Numbers k such that 1 is the smallest decimal digit of k^3.

Original entry on oeis.org

1, 5, 6, 8, 11, 12, 13, 17, 21, 23, 24, 25, 26, 27, 28, 31, 39, 41, 44, 45, 49, 51, 53, 54, 55, 56, 57, 58, 61, 64, 68, 71, 75, 81, 82, 83, 85, 88, 91, 97, 98, 104, 105, 108, 111, 113, 114, 119, 121, 122, 125, 129, 136, 137, 139, 146, 147, 148, 151, 153, 156

Offset: 1

Colin Barker, Aug 28 2017

			11 is in the sequence because 11^3 = 1331, the smallest decimal digit of which is 1.

Cf. A291639, A291641, A291642, A291643, A291644.

select(k->vecmin(digits(k^3))==1, vector(500, k, k))

A291641 Numbers k such that 2 is the smallest decimal digit of k^3.

Original entry on oeis.org

3, 9, 14, 18, 29, 32, 35, 38, 62, 65, 66, 72, 78, 132, 133, 142, 144, 154, 155, 166, 177, 178, 188, 196, 198, 203, 282, 286, 288, 295, 296, 298, 305, 307, 322, 323, 328, 337, 357, 359, 362, 364, 375, 377, 382, 404, 412, 425, 444, 453, 463, 607, 609, 616, 632

Offset: 1

Colin Barker, Aug 28 2017

			38 is in the sequence because 38^3 = 54872, the smallest decimal digit of which is 2.

Cf. A291639, A291640, A291642, A291643, A291644.

Select[Range[700],Min[IntegerDigits[#^3]]==2&] (* Harvey P. Dale, Feb 23 2023 *)

select(k->vecmin(digits(k^3))==2, vector(1000, k, k))

A333206 a(n) is the least decimal digit of n^3.

Original entry on oeis.org

0, 1, 8, 2, 4, 1, 1, 3, 1, 2, 0, 1, 1, 1, 2, 3, 0, 1, 2, 5, 0, 1, 0, 1, 1, 1, 1, 1, 1, 2, 0, 1, 2, 3, 0, 2, 4, 0, 2, 1, 0, 1, 0, 0, 1, 1, 3, 0, 0, 1, 0, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 2, 0, 1, 2, 2, 0, 1, 0, 0, 1, 2, 0, 0, 1, 3, 3, 2, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 0, 0, 1, 6, 0, 0, 3, 3, 1, 1

Offset: 0

Robert Israel, Mar 12 2020

Dean Hickerson found an infinite sequence of n such that a(n) > 0 (see Guy, sec F24). Are there infinitely many such that a(n) > 1? If not, what is the greatest n with a(n)=k for each k > 1?

Heuristically, we should expect on the order of ((10-m)^3/100)^d terms n with d digits and a(n) >= m. Since 5^3/100 > 1 > 4^3/100 we should expect infinitely many terms with a(n) >= 5 but only finitely many terms with a(n) >= 6. See A291644 for a(n) = 5. There are only two n <= 10^6 with a(n) >= 6, namely a(2) = 8 and a(92) = 6.

			The least digit of 6^3=216 is 1, so a(6)=1.

R. Guy, Unsolved Problems in Number Theory (Third edition), Springer 2004.

Robert Israel, Table of n, a(n) for n = 0..10000

Cf. A052044, A054054, A269250, A291639, A291640, A291641, A291642, A291643, A291644.

seq(min(convert(n^3,base,10)),n=0..200);

a(n) = A054054(n^3).

cp's OEIS Frontend

A291639 Numbers k such that 0 is the smallest decimal digit of k^3.

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A291642 Numbers k such that 3 is the smallest decimal digit of k^3.

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A291643 Numbers k such that 4 is the smallest decimal digit of k^3.

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A291640 Numbers k such that 1 is the smallest decimal digit of k^3.

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A291641 Numbers k such that 2 is the smallest decimal digit of k^3.

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A333206 a(n) is the least decimal digit of n^3.

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