A144688 -id:A144688 - cp's OEIS frontend

A235500 Numbers k such that k and all its prefixes are a multiple of the difference between their length and their last digit.

0, 2, 20, 21, 23, 24, 202, 204, 210, 212, 214, 216, 232, 234, 240, 242, 244, 246, 2020, 2022, 2023, 2025, 2026, 2028, 2040, 2042, 2043, 2045, 2046, 2048, 2100, 2102, 2103, 2105, 2106, 2108, 2120, 2121, 2122, 2123, 2125, 2126, 2127, 2128, 2140, 2142, 2143

Offset: 1

Giovanni Resta, Jan 11 2014

The sequence has 1117896 terms, all beginning with 2, apart 0. The largest term is 2160088425040528890600488466.

			2128 is a term because 2 is divisible by (1-2), 21 by (2-1), 212 by (3-1) and 2128 by (4-8).

Giovanni Resta, Table of n, a(n) for n = 1..10000

Cf. A144688.

r[v_, nd_] := Block[{w=10*v, d=nd+1}, Do[ If[w < 10^4 && i != d && Mod[w, d-i] == 0, Sow@ w; r[w, d]]; w++, {i, 0, 9}]]; Union[{0,2}, Reap[r[2, 1]][[2, 1]]] (* terms < 10^4 *)

A324022 Zeroless "magic" numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 14, 16, 18, 22, 24, 26, 28, 32, 34, 36, 38, 42, 44, 46, 48, 52, 54, 56, 58, 62, 64, 66, 68, 72, 74, 76, 78, 82, 84, 86, 88, 92, 94, 96, 98, 123, 126, 129, 141, 144, 147, 162, 165, 168, 183, 186, 189, 222, 225, 228, 243, 246, 249, 261, 264, 267, 282, 285

Offset: 1

Seiichi Manyama, Sep 01 2019

Intersection of A052382 and A144688.

The 2157th and largest term is the 9-digit number 987654564.

			98        = 2 * 49,
987       = 3 * 329,
9876      = 4 * 2469,
98765     = 5 * 19753,
987654    = 6 * 164609,
9876545   = 7 * 1410935,
98765456  = 8 * 12345682,
987654564 = 9 * 109739396.
So 987654564 is a term.

Seiichi Manyama, Table of n, a(n) for n = 1..2157
Wikipedia, Polydivisible number

Cf. A052382, A144688, A324019, A324020.

cp's OEIS Frontend

A235500 Numbers k such that k and all its prefixes are a multiple of the difference between their length and their last digit.

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