OFFSET
1,1
COMMENTS
For any prime p, p +- digitsum(p, base b) can't be prime unless the base b is even, since in an odd base, an odd number always has an odd digit sum (powers of b are congruent to b (mod 2)), so p +- digitsum(p, base b) is even for odd b. This sequence is for b = 10 (where "-" is also excluded, see comment in A243442), see A243441 for b = 2. - M. F. Hasler, Nov 06 2018
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
EXAMPLE
a(9) = prime 97 because 97 + sum-of-digits(97) = 97 + 16 = 113 also a prime.
MAPLE
select(n -> isprime(n) and isprime(n + convert(convert(n, base, 10), `+`)), [$1..10^4]); # Robert Israel, Aug 10 2014
MATHEMATICA
Select[Prime[Range[500]], PrimeQ[#+Total[IntegerDigits[#]]]&] (* Harvey P. Dale, Oct 03 2011 *)
PROG
(PARI) select( is(p)=isprime(p+sumdigits(p))&&isprime(p), primes([0, 2000])) \\ M. F. Hasler, Aug 08 2014, edited Nov 09 2018
(Haskell)
a048519 n = a048519_list !! (n-1)
a048519_list = map a000040 $ filter ((== 1) . a010051' . a065073) [1..]
-- Reinhard Zumkeller, Sep 27 2014
(Magma) [p: p in PrimesUpTo(1200) | IsPrime(q) where q is p+&+Intseq(p)]; // Vincenzo Librandi, Jan 30 2018
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Patrick De Geest, May 15 1999
STATUS
approved