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

1,1

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

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

Links

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

Formula

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

Example

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

Maple

P:=proc(n) local i, j, k, w; for i from 1 by 1 to n do w:=0; k:=ithprime(i); j:=k; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if isprime(j+w) then print(j); fi; od; end: P(1000); # Paolo P. Lava, Mar 02 2009
# Alternate:
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

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.

Sequence in context: A145482 A167497 A068579 * A288878 A102907 A235479

Adjacent sequences: A048516 A048517 A048518 * A048520 A048521 A048522

Keyword

nonn,base

Author

Patrick De Geest, May 15 1999

Status

approved