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

3, 9, 10, 14, 15, 21, 26, 33, 35, 38, 39, 50, 51, 62, 65, 66, 69, 70, 77, 78, 86, 91, 93, 95, 102, 110, 111, 114, 122, 123, 129, 130, 133, 138, 146, 154, 159, 161, 170, 174, 190, 201, 203, 206, 209, 213, 215, 217, 218, 221, 222, 230, 238, 249, 258, 278, 282, 287

Offset: 1

Author

Paolo P. Lava, Sep 18 2013

Keywords

• nonn

Examples

			15 is in the list because 15’ = 8 and 15 - 8 = 7 that is prime.
		

Links

• Paolo P. Lava, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A003415, A165561, A165562, A229270-A229272.

Programs

Maple

with(numtheory); P:=proc(q) local a,n,p; for n from 1 to q do
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);

Python

from sympy import isprime, factorint
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