A349485 Moran numbers whose arithmetic derivative is also a Moran number (A001101).

18, 27, 153, 803, 1101, 1503, 1926, 3070, 3077, 3546, 4577, 6246, 6315, 8717, 10566, 11646, 14093, 15310, 15426, 18456, 24936, 30617, 33576, 34326, 43079, 50418, 59026, 62004, 69781, 71009, 71802, 72587, 74616, 77593, 80118, 94056, 110138, 111546, 112626, 113166

Offset: 1

Author

Marius A. Burtea, Nov 20 2021

Keywords

• nonn
• base

Comments

Conjecture: The sequence is infinite.

Examples

			18 = A001101(1) and 18' = 21 = A001101(2), so 18 is a term.
153 = A001101(13) and 153' = 111 = A001101(8), so 153 is a term.
		

Crossrefs

Cf. A001101 (Moran number), A003415 (arithmetic derivative).

Programs

Magma

f:=func; moran:=func; [n:n in [2..114000]| moran(n) and moran(Floor(f(n)))];

Mathematica

moranQ[n_] := PrimeQ[n / Plus @@ IntegerDigits[n]]; d[n_] := n * Plus @@ ((Last[#]/First[#]) & /@ FactorInteger[n]); Select[Range[120000], And @@ moranQ /@ {#, d[#]} &] (* Amiram Eldar, Nov 20 2021 *)