A048378 -id:A048378 - cp's OEIS frontend

A270263 Integers divisible by the last row of their "upside-down" triangle (see comments).

10, 12, 20, 21, 23, 24, 30, 32, 34, 36, 40, 42, 43, 45, 46, 48, 50, 54, 56, 60, 63, 64, 65, 67, 68, 69, 70, 76, 78, 80, 84, 86, 87, 89, 90, 96, 98, 100, 102, 110, 112, 114, 120, 122, 124, 126, 130, 132, 134, 136, 138, 140, 142, 144, 146, 148, 150, 152, 156, 158, 160, 162, 168, 170, 172, 174, 180, 182, 190, 192, 200, 201, 203, 204, 211, 213, 214, 216, 220, 221, 223, 224, 225, 228, 230, 231, 233, 235, 236, 237, 240, 241, 243, 244, 245, 247, 248, 249, 250, 251

Offset: 1

Eric Angelini and Lars Blomberg, Mar 14 2016

2.0.1.4     2.0.1.5     2.0.1.6     2.2.1.6
.2.1.3       2.1.4       2.1.5       0.1.5
..1.2         1.3         1.4         1.4
...1           2           3           3
A digit "d" of such an "upside-down" triangle is the result of the absolute digit-differences of the two digits above "d". The last row has one digit. If this digit divides the top row integer, we have a hit. No hit here for 2015 (as 2 doesn't divide 2015) and no hit for 2216 (as 3 doesn't divide 2216), but two hits for 2014 and 2016. No division by zero is accepted. Leading zeros below the first row must be kept if they arise.

This is not A048378.

A327709 The numbers n that are a multiple or divisor of A053392(n), the concatenation of the sum of the consecutive digits of n.

Original entry on oeis.org

10, 12, 18, 20, 21, 24, 27, 30, 36, 40, 42, 45, 48, 50, 54, 60, 63, 70, 72, 80, 81, 84, 90, 100, 105, 108, 182, 200, 236, 261, 300, 400, 405, 445, 455, 500, 600, 616, 700, 750, 800, 900, 1000, 1305, 1567, 2000, 3000, 4000

Offset: 1

Scott R. Shannon, Feb 24 2020

As A053392(n) can be either larger or smaller than n this sequence lists n when it is either a multiple or a divisor of A053392(n). In the majority of terms n is a multiple of A053392(n); the first case where n is a divisor is a(27) = 182, where A053392(182) = 910.

All numbers of the form n = k*10^t, with k,t>=1 are in the sequence, as are numbers n = 75*10^t, with t>=1. Also present are numbers of the form n = 444...445 which have A053392 values like 888...889, for which n = 5*A053392(n). Similarly numbers of the form n = 444...455, which have A053392 values like 888...8910, for which A053392(n) = 2*n. For numbers up to 10^10 the largest term which is not one of these forms is a(120) = 654653884, which divides A053392(654653884) = 11910118111612.

			a(7) = 27 is a term as A053392(27) = 9, and 27 is a multiple of 9.
a(27) = 182 is a term as A053392(182) = 910, and 182 is a divisor of 910.
a(29) = 236 is a term as A053392(236) = 59, and 236 is a multiple of 59.

Giovanni Resta, Table of n, a(n) for n = 1..180 (first 137 terms from Scott R. Shannon)

Cf. A053392, A048378 (digit difference instead of sum).

cp's OEIS Frontend

A270263 Integers divisible by the last row of their "upside-down" triangle (see comments).

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