A328207 Starts of runs of 4 consecutive factorial base Niven numbers (A118363).

9320542, 11397166, 29048470, 29394574, 40469902, 40816006, 58467310, 72657574, 84079006, 101730310, 178911502, 200716054, 283088806, 479329774, 485213542, 499403806, 528476542, 530553166, 544743430, 559625902, 559972006, 574162270, 603235006, 617425270, 641652550

Offset: 1

Author

Amiram Eldar, Oct 07 2019

Keywords

• nonn
• base

Comments

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

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

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..512
• 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, 3], fnQ]; Select[Range[10^8], aQ] (* after Jean-François Alcover at A034968 *)