|
%I #14 Jul 07 2023 15:06:46
%S 1,8,26,35,90,122,244,245,300,384,440,510,722,804,844,845,935,944,984,
%T 1014,1079,1224,1232,1444,1445,1518,1584,1589,1727,1728,1736,1770,
%U 1880,2159,2184,2232,2240,2528,2540,2650,2820,2980,3032,3263,3640,4199,4328,4848
%N Numbers m such that m and m+1 are consecutive factorial base Niven numbers (A118363).
%C Dahlenberg & Edgar proved that this sequence is infinite.
%H Amiram Eldar, <a href="/A328205/b328205.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Dahlenberg and Tom Edgar, <a href="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>.
%e 8 is in the sequence since both 8 and 9 are in A118363. A034968(8) = 2 is a divisor of 8 and A034968(9) = 3 is a divisor of 9.
%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, 1], fnQ]; Select[Range[5000], aQ] (* after _Jean-François Alcover_ at A034968 *)
%Y Cf. A007623, A034968, A118363.
%K nonn,base
%O 1,2
%A _Amiram Eldar_, Oct 07 2019
|
