A328206 Starts of runs of 3 consecutive factorial base Niven numbers (A118363).

244, 844, 1444, 1727, 5164, 5764, 5950, 10084, 10967, 13583, 15190, 20207, 21130, 22048, 40444, 40535, 41044, 45364, 45550, 56015, 60730, 62848, 63479, 80644, 91408, 132208, 153340, 163799, 173008, 176110, 178007, 195983, 242368, 280852, 283168, 363004, 363604

Offset: 1

Author

Amiram Eldar, Oct 07 2019

Keywords

• nonn
• base

Comments

Dahlenberg & Edgar proved that this sequence is infinite.

Examples

			244 is in the sequence since 244, 245 and 246 are in A118363. A034968(244) = 4 is a divisor of 244, A034968(245) = 5 is a divisor of 245, and A034968(246) = 3 is a divisor of 246.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Paul Dahlenberg and Tom Edgar, Consecutive factorial base Niven numbers, Fibonacci Quarterly, Vol. 56, No. 2 (2018), pp. 163-166; alternative link. [Wayback Machine link]

Crossrefs

Cf. A007623, A034968, A118363.

Programs

Mathematica

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, 2], fnQ]; Select[Range[400000], aQ] (* after Jean-François Alcover at A034968 *)