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

1,1

Comments

Dahlenberg & Edgar proved that this sequence is infinite.

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]

Example

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.

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 *)

Crossrefs

Cf. A007623, A034968, A118363.

Sequence in context: A201998 A234262 A031786 * A135409 A203349 A262092

Adjacent sequences: A328203 A328204 A328205 * A328207 A328208 A328209

Keyword

nonn,base

Author

Amiram Eldar, Oct 07 2019

Status

approved