A328205 Numbers m such that m and m+1 are consecutive factorial base Niven numbers (A118363).

1, 8, 26, 35, 90, 122, 244, 245, 300, 384, 440, 510, 722, 804, 844, 845, 935, 944, 984, 1014, 1079, 1224, 1232, 1444, 1445, 1518, 1584, 1589, 1727, 1728, 1736, 1770, 1880, 2159, 2184, 2232, 2240, 2528, 2540, 2650, 2820, 2980, 3032, 3263, 3640, 4199, 4328, 4848

Offset: 1

Author

Amiram Eldar, Oct 07 2019

Keywords

• nonn
• base

Comments

Dahlenberg & Edgar proved that this sequence is infinite.

Examples

			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.
		

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.

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, 1], fnQ]; Select[Range[5000], aQ] (* after Jean-François Alcover at A034968 *)