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A165562
Numbers n for which n+n' is prime, n' being the arithmetic derivative of n.
8
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).
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
Sequence in context: A281974 A080324 A332951 * A302796 A302797 A355530
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Terms verified by Alonso del Arte, Oct 30 2009
STATUS
approved