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

1,1

Comments

Conjecture: The sequence is infinite.

Links

Table of n, a(n) for n=1..40.

Example

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.

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 *)

Prog

(Magma) f:=func<n |n le 1 select 0 else n*(&+[Factorisation(n)[i][2] / Factorisation(n)[i][1]: i in [1..#Factorisation(n)]]) >; moran:=func<n|n mod &+Intseq(n) eq 0 and IsPrime(n div &+Intseq(n))>; [n:n in [2..114000]| moran(n) and moran(Floor(f(n)))];

Crossrefs

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

Sequence in context: A279108 A038632 A138336 * A166630 A154920 A094224

Adjacent sequences: A349482 A349483 A349484 * A349486 A349487 A349488

Keyword

nonn,base

Author

Marius A. Burtea, Nov 20 2021

Status

approved