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

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

1,1

Links

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

Example

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

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);

Prog

(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

Crossrefs

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

Sequence in context: A319497 A036119 A211185 * A363954 A050852 A066887

Adjacent sequences: A229266 A229267 A229268 * A229270 A229271 A229272

Keyword

nonn

Author

Paolo P. Lava, Sep 18 2013

Status

approved