A109982 - OEIS

%I #11 Sep 15 2019 11:56:31

%S 11,41,67,83,157,179,191,241,283,331,353,401,461,599,739,773,797,919,

%T 991,10079,10169,10433,10457,10589,10631,10723,10853,10909,11311,

%U 11447,11867,11953,12097,12143,12301,12457,12479,12503,12547,12763,13003

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

%H Harvey P. Dale, <a href="/A109982/b109982.txt">Table of n, a(n) for n = 1..1000</a>

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

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

%t 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 *)

%Y 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.

%K base,nonn

%O 1,1

%A _Zak Seidov_, Jul 06 2005