A165562 - OEIS

%I #15 Feb 04 2022 10:36:59

%S 2,6,10,14,15,21,26,30,33,34,35,38,42,46,51,55,57,58,65,66,74,78,85,

%T 86,93,102,110,111,118,123,141,143,145,155,158,161,166,177,178,182,

%U 185,186,194,201,203,205,206,209,210,215,221,230,246,254,258,267,278,282,290

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

%C 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).

%H T. D. Noe, <a href="/A165562/b165562.txt">Table of n, a(n) for n = 1..1000</a>

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

%p with(numtheory);

%p P:= proc(n)

%p local a,i,p,pfs;

%p for i from 1 to n do

%p pfs:=ifactors(i)[2]; a:=i*add(op(2,p)/op(1,p),p=pfs);

%p if isprime(a+i) then print(i); fi;

%p od;

%p end:

%p P(1000);

%p # alternative

%p isA165562 := proc(n)

%p     isprime(A129283(n)) ;

%p end proc:

%p for n from 1 to 1000 do

%p     if isA165562(n) then

%p         printf("%d,",n) ;

%p     end if;

%p end do: # _R. J. Mathar_, Feb 04 2022

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

%o (Python)

%o from sympy import isprime, factorint

%o 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

%Y Cf. A003415, A165561.

%K easy,nonn

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Sep 25 2009

%E Terms verified by _Alonso del Arte_, Oct 30 2009