A296107 Twin prime pairs both of which have the same number of prime digits.

3, 5, 5, 7, 29, 31, 809, 811, 1229, 1231, 1289, 1291, 2129, 2131, 2309, 2311, 2729, 2731, 2789, 2791, 2999, 3001, 3299, 3301, 3329, 3331, 3389, 3391, 3929, 3931, 4229, 4231, 5009, 5011, 5099, 5101, 6089, 6091, 6299, 6301, 6689, 6691, 7589, 7591, 8009, 8011

Offset: 1

Author

Harvey P. Dale, Dec 04 2017

Keywords

• nonn
• base

Comments

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

Examples

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

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A158284.

Programs

Mathematica

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

PARI

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