A109981 Primes such that both the sum of digits and the number of digits are primes.

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

Offset: 1

Author

Zak Seidov, Jul 06 2005

Keywords

• base
• nonn

Comments

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

Examples

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

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.

Crossrefs

Cf. A046704, A088136.

Cf. A010051, A055642.

Programs

Haskell

a109981 n = a109981_list !! (n-1)
a109981_list = filter ((== 1) . a010051' . a055642) a046704_list
-- Reinhard Zumkeller, Nov 16 2012

Mathematica

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