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

1,2

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.

Example

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.

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 *)

Crossrefs

Cf. A007623, A034968, A118363.

Sequence in context: A345205 A063560 A265104 * A304910 A271989 A069952

Adjacent sequences: A328202 A328203 A328204 * A328206 A328207 A328208

Keyword

nonn,base

Author

Amiram Eldar, Oct 07 2019

Status

approved