

A046704


Additive primes: sum of digits is a prime.


47



2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89, 101, 113, 131, 137, 139, 151, 157, 173, 179, 191, 193, 197, 199, 223, 227, 229, 241, 263, 269, 281, 283, 311, 313, 317, 331, 337, 353, 359, 373, 379, 397, 401, 409, 421, 443, 449, 461, 463, 467, 487, 557, 571, 577, 593
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OFFSET

1,1


COMMENTS

Sum_{a(n) < x} 1/a(n) is asymptotic to (3/2)*log(log(log(x))) as x > infinity; see Harman (2012). Thus the sequence is infinite.  Jonathan Sondow, Jun 07 2012
Harman 2012 also shows, under a conjecture about primes in short intervals, that a(n) ~ 3/2 * n/(log n log log n).  Charles R Greathouse IV, Nov 17 2014


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Glyn Harman, Counting primes whose sum of digits is prime, J. Integer Seq., 15 (2012), Article 12.2.2.
Glyn Harman, Primes whose sum of digits is prime and metric number theory, Bull. Lond. Math. Soc. 44:5 (2012), pp. 10421049.


EXAMPLE

The digit sums of 11 and 13 are 1+1=2 and 1+3=4. Since 2 is prime and 4 is not, 11 is a member and 13 is not.  Jonathan Sondow, Jun 07 2012


MAPLE

select(n > isprime(n) and isprime(convert(convert(n, base, 10), `+`)), [2, seq(2*i+1, i=1..1000)]); # Robert Israel, Nov 17 2014


MATHEMATICA

Select[Prime[Range[100000]], PrimeQ[Apply[Plus, IntegerDigits[ # ]]]&]


PROG

(PARI) isA046704(n)={local(s, m); s=0; m=n; while(m>0, s=s+m%10; m=floor(m/10)); isprime(n) & isprime(s)} \\ Michael B. Porter, Oct 18 2009
(PARI) is(n)=isprime(n) && isprime(sumdigits(n)) \\ Charles R Greathouse IV, Dec 26 2013
(MAGMA) [ p: p in PrimesUpTo(600)  IsPrime(&+Intseq(p)) ]; // Bruno Berselli, Jul 08 2011
(Haskell)
a046704 n = a046704_list !! (n1)
a046704_list = filter ((== 1) . a010051 . a007953) a000040_list
 Reinhard Zumkeller, Nov 13 2011


CROSSREFS

Indices of additive primes are in A075177.
Cf. A046703, A119450 = Primes with odd digit sum, A081092 = Primes with prime binary digit sum, A104213 = Primes with nonprime digit sum.
Cf. A007953, A010051; intersection of A028834 and A000040.
Sequence in context: A087521 A078403 A129945 * A089392 A089695 A070027
Adjacent sequences: A046701 A046702 A046703 * A046705 A046706 A046707


KEYWORD

base,nonn


AUTHOR

Felice Russo


STATUS

approved



