A266181 -id:A266181 - cp's OEIS frontend

A343405 Numbers k such that A343404(k) = k.

0, 1, 5, 6, 11, 12, 17, 18, 23, 24, 29, 36, 65, 72, 101, 108, 137, 144, 173, 209, 210, 419, 420, 629, 630, 839, 840, 1049, 1050, 1259, 1260, 1469, 1470, 1679, 1680, 1889, 1890, 2099, 2100, 2309, 2939, 4200, 5670, 7140, 8609, 10079, 11340, 12810, 14280, 15749

Offset: 1

Rémy Sigrist, Apr 14 2021

If m belongs to this sequence, then the number obtained by removing the leading digit from the expansion of m in primary base also belongs to this sequence.
So the terms of the sequence can be mapped on a tree with root 0 (see illustration in Links section).
Is this sequence infinite?

			A343404(2099) = 2099, so 2099 belongs to this sequence.

Rémy Sigrist, Table of n, a(n) for n = 1..1000
Rémy Sigrist, Illustration of the terms < 2*3*5*7*11
Rémy Sigrist, PARI program for A343405
Index entries for sequences related to primorial base

Cf. A266181, A319599, A343404.

PARI
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A319599 Numbers k such that k mod (2, 3, 4, ... , i+1) = (d_i, d_i-1, ..., d_1), where d_1, d_2, ..., d_i are the digits of k, with MSD(k) = d_1 and LSD(k) = d_i.

Original entry on oeis.org

0, 1, 10, 20, 1101, 1121, 11311, 31101, 40210, 340210, 4620020, 5431101, 7211311, 12040210, 24120020, 151651121, 165631101, 1135531101, 8084220020, 9117311311, 894105331101

Offset: 0

Paolo P. Lava, Sep 24 2018

			a(11) = 5431101 because:
5431101 mod 2 = 1, 5431101 mod 3 = 0, 5431101 mod 4 = 1,
5431101 mod 5 = 1, 5431101 mod 6 = 3, 5431101 mod 7 = 4,
5431101 mod 8 = 5.

Cf. A266181, A284815.

P:=proc(q) local a,i,j,n,ok; print(0); print(1); for n from 1 to q do
for i from 0 to 1 do a:=10*n+i; ok:=1; for j from 1 to ilog10(a)+1 do
if (a mod 10)<>((10*n+i) mod (j+1)) then ok:=0; break; else
a:=trunc(a/10); fi; od; if ok=1 then print(10*n+i); break; fi;
od; od; end: P(10^12);

cp's OEIS Frontend

A343405 Numbers k such that A343404(k) = k.

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