cp's OEIS Frontend

A229269 Numbers k for which k - k' is prime, k' being the arithmetic derivative of k.

%I A229269 #13 Jul 28 2025 20:48:17
%S A229269 3,9,10,14,15,21,26,33,35,38,39,50,51,62,65,66,69,70,77,78,86,91,93,
%T A229269 95,102,110,111,114,122,123,129,130,133,138,146,154,159,161,170,174,
%U A229269 190,201,203,206,209,213,215,217,218,221,222,230,238,249,258,278,282,287
%N A229269 Numbers k for which k - k' is prime, k' being the arithmetic derivative of k.
%H A229269 Paolo P. Lava, <a href="/A229269/b229269.txt">Table of n, a(n) for n = 1..1000</a>
%e A229269 15 is in the list because 15’ = 8 and 15 - 8 = 7 that is prime.
%p A229269 with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
%p A229269 a:=n*add(op(2,p)/op(1,p),p=ifactors(n)[2]); if isprime(n-a) then print(n); fi; od; end: P(10^5);
%o A229269 (Python)
%o A229269 from sympy import isprime, factorint
%o A229269 A229269 = [n for n in range(1,10**4) if isprime(n-sum([int(n*e/p) for p,e in factorint(n).items()]))] # _Chai Wah Wu_, Aug 21 2014
%Y A229269 Cf. A003415, A165561, A165562, A229270-A229272.
%K A229269 nonn
%O A229269 1,1
%A A229269 _Paolo P. Lava_, Sep 18 2013