A048519 Prime plus its digit sum equals a prime.

11, 13, 19, 37, 53, 59, 71, 73, 97, 101, 103, 127, 149, 163, 167, 181, 233, 257, 271, 277, 293, 307, 367, 383, 389, 419, 431, 433, 479, 499, 509, 547, 563, 587, 617, 631, 701, 727, 743, 787, 811, 839, 857, 859, 947, 1009, 1049, 1061, 1087, 1153, 1171

Offset: 1

Author

Patrick De Geest, May 15 1999

Keywords

• nonn
• base

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

See subsequence A048523 for primes which only once give another prime under iteration of A062028, and A048524 .. A048527, A320878 .. A320880 for primes starting longer chains. See A090009 for their initial terms, starting the earliest chain of given length. - M. F. Hasler, Nov 09 2018

Examples

			a(9) = prime 97 because 97 + sum-of-digits(97) = 97 + 16 = 113 also a prime.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A007953 (digit sum), A062028 (n + digit sum of n), A047791 (A062028(n) is prime), A048520.

Cf. A006378, A107740.

Cf. A000040, A010051, A065073.

Cf. A048523 .. A048527, A320878, A320879, A320880, A090009.

Programs

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

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 *)

PARI

select( is(p)=isprime(p+sumdigits(p))&&isprime(p), primes([0,2000])) \\ M. F. Hasler, Aug 08 2014, edited Nov 09 2018

Formula

Primes in A047791, i.e., intersection of A047791 and A000040. - M. F. Hasler, Nov 08 2018