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A046704 Additive primes: sum of digits is a prime. 45
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 (list; graph; refs; listen; history; text; internal format)
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

REFERENCES

Glyn Harman, Primes whose sum of digits is prime and metric number theory, Bull. Lond. Math. Soc. 44:5 (2012), pp. 1042-1049.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

G. Harman, Counting primes whose sum of digits is prime, J. Integer Seq., 15 (2012), Article 12.2.2.

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

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 !! (n-1)

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

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Last modified April 18 19:33 EDT 2014. Contains 240733 sequences.