The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A342304 k-digit positive numbers exactly one of whose substrings is divisible by k. 1
 1, 2, 3, 4, 5, 6, 7, 8, 9, 21, 23, 25, 27, 29, 41, 43, 45, 47, 49, 61, 63, 65, 67, 69, 81, 83, 85, 87, 89, 101, 104, 107, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 125, 128, 131, 134, 137, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 152, 155, 158, 161 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Inspired by the 413th problem of Project Euler (see link) where such a number is called "one-child number". There are k*(k+1)/2 substrings.  All are considered, even when some are duplicates as strings or as numbers (see the Example section). 0 is always divisible by k so any number with two or more 0 digits is not a term. - Kevin Ryde, Mar 08 2021 The 2-digit terms are odd. The number of k-digit terms for k = 1, 2, 3 is respectively 9, 20, 360. From Robert Israel, Mar 11 2021: (Start) 5-digit terms are numbers starting with 5, and with no other digits 5 or 0. There are no 10-digit terms. (End) LINKS Robert Israel, Table of n, a(n) for n = 1..10000 Project Euler, Problem 413: One-child Numbers. EXAMPLE 107 is a 3-digit one-child number since among its substrings 1, 0, 7, 10, 07, 107 only 0 is divisible by 3. 222 is a 3-digit one-child number since among its substrings 2, 2, 2, 22, 22, 222 only 222 is divisible by 3. 572 is not a 3-digit one-child number, since among its substrings 5, 7, 1, 57, 72, 572 both 57 and 72 are divisible by 3. 616 is not a 3-digit one-child number, since among its substrings 6, 1, 6, 61, 16, 616 the two 6's are both divisible by 3. MAPLE filter:= proc(n) local L, d, i, j, k, ct, x;   L:= convert(n, base, 10);   d:= nops(L);   ct:= 0:   for i from 1 to d do     for j from i to d do       x:= add(L[k]*10^(k-i), k=i..j);       if x mod d = 0 then ct:= ct+1; if ct = 2 then return false fi fi;   od od;   evalb(ct = 1) end proc: select(filter, [\$1..200]); # Robert Israel, Mar 11 2021 CROSSREFS Cf. A063527. Sequence in context: A069571 A039173 A103951 * A098951 A097962 A247813 Adjacent sequences:  A342299 A342302 A342303 * A342306 A342307 A342308 KEYWORD nonn,base AUTHOR Bernard Schott, Mar 08 2021 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 13 16:56 EDT 2021. Contains 343862 sequences. (Running on oeis4.)