A165562 Numbers n for which n+n' is prime, n' being the arithmetic derivative of n.

2, 6, 10, 14, 15, 21, 26, 30, 33, 34, 35, 38, 42, 46, 51, 55, 57, 58, 65, 66, 74, 78, 85, 86, 93, 102, 110, 111, 118, 123, 141, 143, 145, 155, 158, 161, 166, 177, 178, 182, 185, 186, 194, 201, 203, 205, 206, 209, 210, 215, 221, 230, 246, 254, 258, 267, 278, 282, 290

Offset

1,1

Comments

The only prime in this sequence is 2. Since it is the only even prime and p' = 1, it is the only prime that added to its derivative can give an odd prime (namely 3).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Example

46 is in the list because: n=46 -> n'=25 -> n+n'=71 that is prime.

Maple

with(numtheory);
P:= proc(n)
local a, i, p, pfs;
for i from 1 to n do
pfs:=ifactors(i)[2]; a:=i*add(op(2, p)/op(1, p), p=pfs);
if isprime(a+i) then print(i); fi;
od;
end:
P(1000);
# alternative
isA165562 := proc(n)
    isprime(A129283(n)) ;
end proc:
for n from 1 to 1000 do
    if isA165562(n) then
        printf("%d, ", n) ;
    end if;
end do: # R. J. Mathar, Feb 04 2022

Mathematica

(*First run the program given in A003415*) A165562 = Select[ Range[ 1000 ], PrimeQ[ # + a[ # ] ] & ]

Prog

(Python)
from sympy import isprime, factorint
A165562 = [n for n in range(1, 10**5) 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.

Sequence in context: A281974 A080324 A332951 * A302796 A302797 A355530

Adjacent sequences: A165559 A165560 A165561 * A165563 A165564 A165565

Keyword

easy,nonn

Author

Paolo P. Lava and Giorgio Balzarotti, Sep 25 2009

Extensions

Terms verified by Alonso del Arte, Oct 30 2009

Status

approved