A328207 - OEIS

%I #14 Jan 05 2025 19:51:41

%S 9320542,11397166,29048470,29394574,40469902,40816006,58467310,

%T 72657574,84079006,101730310,178911502,200716054,283088806,479329774,

%U 485213542,499403806,528476542,530553166,544743430,559625902,559972006,574162270,603235006,617425270,641652550

%N Starts of runs of 4 consecutive factorial base Niven numbers (A118363).

%C Dahlenberg & Edgar proved that this sequence is infinite and that there are no consecutive runs of 5 or more factorial base Niven numbers.

%C a(1)-a(18) were calculated by Dahlenberg & Edgar.

%H Amiram Eldar, <a href="/A328207/b328207.txt">Table of n, a(n) for n = 1..512</a>

%H Paul Dahlenberg and Tom Edgar, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Abstracts/56-2/dalenberg.pdf">Consecutive factorial base Niven numbers</a>, Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166; <a href="https://web.archive.org/web/20211018191809/https://community.plu.edu/~edgartj/consecutivefactniven.pdf">alternative link</a>. [Wayback Machine link]

%e 9320542 is in the sequence since 9320542, 9320543, 9320544 and 9320545 are all in A118363: A034968(9320542) = 22 is a divisor of 9320542, A034968(9320543) = 23 is a divisor of 9320543, A034968(9320544) = 18 is a divisor of 9320544, and A034968(9320545) = 19 is a divisor of 9320545.

%t sf[n_] := Module[{s = 0, i = 2, k = n}, While[k > 0, k = Floor[n/i!]; s = s + (i - 1)*k; i++]; n - s]; fnQ[n_] := Divisible[n, sf[n]]; aQ[n_] := AllTrue[n + Range[0, 3], fnQ]; Select[Range[10^8], aQ] (* after _Jean-François Alcover_ at A034968 *)

%Y Cf. A007623, A034968, A118363.

%K nonn,base

%O 1,1

%A _Amiram Eldar_, Oct 07 2019