A029519 - OEIS

%I #40 Jul 26 2021 01:45:34

%S 1,3,7,17,27,63,92883,1556671

%N Numbers k such that k divides the (left) concatenation of all numbers <= k written in base 2 (most significant digit on right).

%C This sequence differs from A061955 in that all least significant zeros are removed before concatenation.

%C No more terms < 10^7. - _Lars Blomberg_, Aug 31 2011

%H <a href="/index/N#concat">Index entries for related sequences</a>

%e 7 is in the sequence as the left concatenation of numbers <= 7 is 7654321 which gives 7654321 -> (111)(011)(101)(001)(11)(01)(1) base 2 -> 1111110111111_2 = 8127, and 7 divides 8127.

%t b = 2; c = {}; Select[Range[10^4], Divisible[FromDigits[c = Join[IntegerDigits[IntegerReverse[#, b], b], c], b], #] &] (* _Robert Price_, Mar 13 2020 *)

%o (J) mkcat =: 13 : 'y +. #. ; #:&.> |.&.#:&.> |. >:i. y'

%o (#~ (= mkcat"0)) >:i. 100x NB. _Stephen Makdisi_, May 03 2018

%Y Cf. A029447-A029470, A029471-A029494, A029495-A029518, A029519-A029542, A061931-A061954, A061955-A061978.

%K nonn,base,more

%O 1,2

%A _Olivier Gérard_

%E Edited and updated by Larry Reeves (larryr(AT)acm.org), Apr 12 2002

%E Additional comments and example from Larry Reeves (larryr(AT)acm.org), May 25 2001

%E Terms verified by _Rick L. Shepherd_, Feb 24 2009

%E 1 more term from _Sean A. Irvine_, Oct 04 2009