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Primes with prime subscripts whose digits are primes, whose digital root is prime, whose sum of digits is prime and whose reversal is also prime.
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%I #6 Nov 27 2016 21:44:26

%S 3,5,353,32732237,35225327,75527537,75535277,75557723,75737723,

%T 75755257,77322233,77752733,322375577,322775737,325725577,325773727,

%U 337735553,352272233,355322777,357333377,357735773,372577727,372753727,375577733,375722377,375727237,377725723,377752723

%N Primes with prime subscripts whose digits are primes, whose digital root is prime, whose sum of digits is prime and whose reversal is also prime.

%C Intersection of A006450, A007500, A019546, A028834 and A078403.

%e 32732237 is in the sequence because 32732237 is the 2016197-th prime number, 2016197 is prime, digits 2, 3 and 7 are primes, 32732237 -> 3 + 2 + 7 + 3 + 2 + 2 + 3 + 7 = 29 (is prime) -> 2 + 9 = 11 -> 1 + 1 = 2, 2 is prime and 73223723 is also prime.

%t Select[Table[Prime[Prime[n]], {n, 1500000}], Complement[IntegerDigits[#1], {2, 3, 5, 7}] == {} && PrimeQ[#1 - 9 Floor[(#1 - 1)/9]] && PrimeQ[Total[IntegerDigits[#1]]] && PrimeQ[FromDigits[Reverse[IntegerDigits[#1]]]] & ]

%Y Cf. A000040, A006450, A007500, A019546, A028834, A078403, A087368.

%K nonn,base

%O 1,1

%A _Ilya Gutkovskiy_, Nov 08 2016