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Primes such that both the sum of digits and the number of digits are primes.
3

%I #8 Jul 13 2013 12:03:21

%S 11,23,29,41,43,47,61,67,83,89,101,113,131,137,139,151,157,173,179,

%T 191,193,197,199,223,227,229,241,263,269,281,283,311,313,317,331,337,

%U 353,359,373,379,397,401,409,421,443,449,461,463,467,487,557,571,577,593

%N Primes such that both the sum of digits and the number of digits are primes.

%C Cf. A046704 Additive primes: sum of digits is a prime, A088136 Primes such that sum of first and last digits is prime.

%H Reinhard Zumkeller, <a href="/A109981/b109981.txt">Table of n, a(n) for n = 1..10000</a>

%H G. Harman, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL15/Harman/harman2.pdf">Counting Primes whose Sum of Digits is Prime</a>, J. Integer Seq., 15 (2012), Article 12.2.2.

%e a(86) = 10037 because both the sum (=11) and number (=5) of digits are primes.

%t Select[Prime[Range[200]], PrimeQ[Length[IntegerDigits[ # ]]]&&PrimeQ[Plus@@IntegerDigits[ # ]]&]

%o (Haskell)

%o a109981 n = a109981_list !! (n-1)

%o a109981_list = filter ((== 1) . a010051' . a055642) a046704_list

%o -- _Reinhard Zumkeller_, Nov 16 2012

%Y Cf. A046704, A088136.

%Y Cf. A010051, A055642.

%K base,nonn

%O 1,1

%A _Zak Seidov_, Jul 06 2005