Lukas R. Mansour - cp's OEIS frontend

User: Lukas R. Mansour

Lukas R. Mansour has authored 2 sequences.

A337391 a(n) is the smallest n-digit number divisible by n^3.

1, 16, 108, 1024, 10000, 100008, 1000188, 10000384, 100000575, 1000000000, 10000001319, 100000001088, 1000000000792, 10000000000536, 100000000001250, 1000000000000000, 10000000000001886, 100000000000001952, 1000000000000003324, 10000000000000000000, 100000000000000008972, 1000000000000000009208

Offset: 1

Lukas R. Mansour, Aug 25 2020

			a(2) = 16, as 16 is the first 2-digit number divisible by 2^3 = 8.
a(3) = 108, as 108 is the first 3-digit number divisible by 3^3 = 27.
a(4) = 1024, as 1024 is the first 4-digit number divisible by 4^3 = 64.
a(5) = 10000, as 10000 is the first 5-digit number divisible by 5^3 = 125.

Cf. A000578, A011557, A053041 (divisible by n), A140317 (divisible by n^2).

Table[n^3 * Ceiling[10^(n - 1)/n^3], {n, 1, 22}] (* Amiram Eldar, Aug 25 2020 *)

a(n) = n^3 * ceil(10^(n-1) / n^3) \\ David A. Corneth, Aug 25 2020

a(n) = n^3 * ceiling(10^(n-1) / n^3). - David A. Corneth, Aug 26 2020

A335151 Numbers m equal to |d_1^k + Sum_{j=2..k} (-1)^j*d_j^k| where d_1 d_2 ... d_k is the decimal expansion of m.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 370, 5295, 8208, 54900, 54901, 417889, 136151168, 9905227379, 282185923199, 2527718648914, 14441494066365380, 14441494066365381, 12317155720243258398, 13393750378644587854

Offset: 1

Lukas R. Mansour, May 25 2020

In other words: m = |digit1^k + digit2^k - digit3^k + digit4^k -...+/- lastdigit^k|, where k is the number of digits. Note that the sign of the first two addends is always positive.
Concept derived from the Armstrong numbers (A005188).
Note that a(15) = a(14) + 1 and a(22) = a(21) + 1. - Chai Wah Wu, May 31 2020

			370 = |3^3 + 7^3 - 0^3|.
5295 = |5^4 + 2^4 - 9^4 + 5^4|.
8208 = |8^4 + 2^4 - 0^4 + 8^4|.
54900 = |5^5 + 4^5 - 9^5 + 0^5 - 0^5|.
54901 = |5^5 + 4^5 - 9^5 + 0^5 - 1^5|.

Cf. A005188, A335205.

ss[n_] := ss[n] = Join[{1}, -(-1)^Range[n-1]]; Select[ Range[0, 500000], (d = IntegerDigits[#]; # == Abs@ Total[d^Length[d] ss@ Length@ d]) &] (* Giovanni Resta, May 25 2020 *)

is(k) = my(v=digits(k)); !k || abs(v[1]^#v + sum(i=2, #v, (-1)^i*v[i]^#v))==k; \\ Jinyuan Wang, May 28 2020

a(18)-a(20) from Giovanni Resta, May 25 2020
a(21)-a(22) from Chai Wah Wu, May 31 2020
a(23)-a(24) from Chai Wah Wu, Jun 01 2020

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User: Lukas R. Mansour

A337391 a(n) is the smallest n-digit number divisible by n^3.

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