A253252 Twin primes with equal number of odd and even digits.

29, 41, 43, 61, 1021, 1049, 1061, 1063, 1229, 1289, 1427, 1429, 1481, 1483, 1487, 1489, 1607, 1609, 1621, 1667, 1669, 2129, 2141, 2143, 2237, 2239, 2309, 2341, 2381, 2383, 2549, 2657

Offset

1,1

Comments

Note that there are the lesser of twin primes (A001359) such as 29, 1049, 1229, 1289, 2129, 2309, 2549, 2729, 2789, 2969, 4019, 4259, 5009,...; the greater of twin primes (A006512) such as 61, 1021, 1621, 2341, 3001, 4051, 4231, 4651, 5281,....; and both terms of twin prime pairs (A001097) such as {41,43}, {1061,1063}, {1427,1429}, {1481,1483}, {1487,1489}, {1607,1609}, {1667,1669}, {2141,2143}, {2237,2239}, {2381,2383}, {2657,2659}, {3461,3463}, {3467,3469}, {3821,3823}, {4091,4093}, {4127,4129}, {4217,4219}, {4271,4273}, {4547,4549}, {4637,4639}, {4721,4723}, {4787,4789}, {4967,4969}, {5021,5023}, ....

Links

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

Maple

Primes:= select(isprime, {seq(2*i+1, i=1..5000)}):
Twins:= map(t -> (t, t+2), Primes intersect map(`-`, Primes, 2)):
filter:= proc(n) local L, Lo, Le;
   if ilog10(n)::even then return false fi;
   L:= convert(n, base, 10);
   Lo, Le:= selectremove(type, L, odd);
   nops(Lo)=nops(Le)
end proc:
sort(convert(select(filter, Twins), list)); # Robert Israel, Jun 08 2015

Mathematica

Select[Prime@ Range@ 500, Plus @@ BitAnd[ IntegerDigits@#, 1] == IntegerLength[#]/2 && Or @@ PrimeQ[# + {2, -2}] &] (* Giovanni Resta, Jun 08 2015 *)

Prog

(PARI) is(n)=my(d=digits(n)); #d%2==0 && sum(i=1, #d, d[i]%2)==#d/2 && isprime(n) && (isprime(n+2)||isprime(n-2)) \\ Charles R Greathouse IV, Jun 08 2015

Crossrefs

Subsequence of A144226.

Cf. A001097, A001359, A006512.

Sequence in context: A108325 A242555 A101007 * A155575 A229059 A330653

Adjacent sequences: A253249 A253250 A253251 * A253253 A253254 A253255

Keyword

base,nonn

Author

Zak Seidov, Jun 07 2015

Status

approved