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Twin prime pairs both of which have the same number of prime digits.
1

%I #9 Dec 05 2017 17:24:22

%S 3,5,5,7,29,31,809,811,1229,1231,1289,1291,2129,2131,2309,2311,2729,

%T 2731,2789,2791,2999,3001,3299,3301,3329,3331,3389,3391,3929,3931,

%U 4229,4231,5009,5011,5099,5101,6089,6091,6299,6301,6689,6691,7589,7591,8009,8011

%N Twin prime pairs both of which have the same number of prime digits.

%C This was essentially the original definition of A158284 but the given terms to that sequence did not match this definition.

%H Charles R Greathouse IV, <a href="/A296107/b296107.txt">Table of n, a(n) for n = 1..10000</a>

%e 3929 and 3931 are twin primes and both have two prime digits.

%t Select[Partition[Prime[Range[2000]],2,1],#[[2]]-#[[1]]==2 && Count[ IntegerDigits[#[[1]]],_?PrimeQ]==Count[IntegerDigits[#[[2]]], _?PrimeQ]&]//Flatten

%o (PARI) ct(n)=my(d=digits(n)); sum(i=1,#d, isprime(d[i]))

%o do(lim)=my(v=List(),p=3); forprime(q=5,lim+2, if(q-p==2 && ct(p)==ct(q), listput(v,p); listput(v,q)); p=q); Vec(v) \\ _Charles R Greathouse IV_, Dec 05 2017

%Y Cf. A158284.

%K nonn,base

%O 1,1

%A _Harvey P. Dale_, Dec 04 2017