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 A328205 Numbers m such that m and m+1 are consecutive factorial base Niven numbers (A118363). 6
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Dahlenberg & Edgar proved that this sequence is infinite. LINKS 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

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Last modified July 28 14:19 EDT 2021. Contains 346335 sequences. (Running on oeis4.)