A109982 Primes p such that index of p, the sum of p's digits and the number of p's digits are all primes.

11, 41, 67, 83, 157, 179, 191, 241, 283, 331, 353, 401, 461, 599, 739, 773, 797, 919, 991, 10079, 10169, 10433, 10457, 10589, 10631, 10723, 10853, 10909, 11311, 11447, 11867, 11953, 12097, 12143, 12301, 12457, 12479, 12503, 12547, 12763, 13003

Offset: 1

Author

Zak Seidov, Jul 06 2005

Keywords

• base
• nonn

Examples

			a(414) = 99551 because its index, 9551, the sum, 29 and number, 5, of digits are all primes.
		

Links

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

Crossrefs

Cf. A046704 Additive primes: sum of digits is a prime, A088136 Primes such that sum of first and last digits is prime, A109981 Primes such that the sum of digits and the number of digits are primes.

Programs

Mathematica

Select[Prime[Range[200]], PrimeQ[Length[IntegerDigits[ # ]]]&&PrimeQ[Plus@@IntegerDigits[ # ]]&]
Select[Prime[Range[1600]],AllTrue[{PrimePi[#],Total[IntegerDigits[#]], IntegerLength[ #]}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 15 2019 *)