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

1,1

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.

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]

Example

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.

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 *)

Crossrefs

Cf. A007623, A034968, A118363.

Sequence in context: A251280 A234395 A204510 * A069376 A281570 A274042

Adjacent sequences: A328204 A328205 A328206 * A328208 A328209 A328210

Keyword

nonn,base

Author

Amiram Eldar, Oct 07 2019

Status

approved