A168575 -id:A168575 - 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))

A286315 Number of representations of 10^n as sum of 8 triangular numbers.

Original entry on oeis.org

8, 1332, 1030302, 1007141184, 1000302990372, 1000781337641904, 1000003970597090004, 1000751615026326041904, 1000203571630368710405892, 1004272191614371538730009600, 1000000970912716777250166728808, 1000834130646589459517111102258880

Offset: 0

Seiichi Manyama, May 06 2017

nonn

a(n) is nearly 10^(3*n) because a(n) is almost (10^n+1)^3.

			a(0) = Sum_{d|2, 2/d == 1 mod 2} d^3 = 2^3 = 8.
a(1) = Sum_{d|11, 11/d == 1 mod 2} d^3 = 11^3 + 1^3 = 1332.
a(2) = Sum_{d|101, 101/d == 1 mod 2} d^3 = 101^3 + 1^3 = 1030302.

Seiichi Manyama, Table of n, a(n) for n = 0..18

Cf. A007331, A062397 (10^n+1), A168575 ((10^n+1)^3), A286314.

a(n) = A007331(10^n + 1).

a(n) = Sum_{d|10^n+1, (10^n+1)/d == 1 mod 2} d^3.

A263613 Palindromic numbers in base 4 that are cubes.

Original entry on oeis.org

0, 1, 1331, 1030301, 1003003001, 1000300030001, 1000030000300001, 1000003000003000001, 1000000300000030000001, 1000000030000000300000001, 1000000003000000003000000001, 1000000000300000000030000000001, 1000000000030000000000300000000001, 1000000000003000000000003000000000001

Offset: 1

N. J. A. Sloane, Oct 22 2015

There is an obvious pattern here, but it is not known how long it will continue.

The cube roots (written in base 4) are 0, 1, 11, 101, 1001, 10001, 100001, 1000001, 10000001, 100000001 (coinciding with A056810 to this point).

Chai Wah Wu, Table of n, a(n) for n = 1..18
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A056810, A168575.

Conjectures from Chai Wah Wu, Dec 25 2023: (Start)
a(n) = 1111*a(n-1) - 112110*a(n-2) + 1111000*a(n-3) - 1000000*a(n-4) for n > 6.
G.f.: x^2*(-7000000*x^4 + 6446000*x^3 - 336330*x^2 + 220*x + 1)/((x - 1)*(10*x - 1)*(100*x - 1)*(1000*x - 1)). (End)

a(11) from Chai Wah Wu, Oct 23 2015

a(12)-a(14) from Chai Wah Wu, Sep 26 2017

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

A286315 Number of representations of 10^n as sum of 8 triangular numbers.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A263613 Palindromic numbers in base 4 that are cubes.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

Extensions