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A155801 Nontrivial "Strobogrammatic" primes, the same "upside-down" in at least one base b with 2 <= b <= 10.

%I A155801 #9 Jul 08 2022 08:21:14
%S A155801 3,5,7,11,13,17,31,37,43,73,101,107,127,181,257,313,443,619,757,1093,
%T A155801 1193,1297,1453,1571,1619,1787,1831,1879,2801,4889,5113,5189,5557,
%U A155801 5869,5981,6211,6827,7607,7759,7919,8191
%N A155801 Nontrivial "Strobogrammatic" primes, the same "upside-down" in at least one base b with 2 <= b <= 10.
%C A155801 I have to say "nontrivial" because every nonnegative integer is strobogrammatic in base 1. Strobogrammatic binary primes == primes in A006995 == A016041. Strobogrammatic primes in base 3 = 13, 757, 1093, 9103, ... == primes strobogrammatic in bases 2 and 3. For bases 2 < k < 8 we have that every strobogrammatic prime in base k must also be strobogrammatic in base 2 and hence palindromic in base 2. Hence we have, for example, strobogrammatic base-4 primes = A056130 = "Palindromic primes in bases 2 and 4."
%C A155801 Strobogrammatic primes in base 5 = 31, 19531, 394501, 472631, ... == primes strobogrammatic in base 2 and base 5. Strobogrammatic primes base 6 = 7, 37, 43, 1297, 55987, ... == primes strobogrammatic in base 2 and base 6. Note that 1101011 (base 6) = 18881 (base 10) which is strobogrammatic base 10 but not prime base 6 nor 10 (though prime base 2). Strobogrammatic primes base 7 = 2801, 134807, this last being strobogrammatic prime in bases 2, 4 and 7. Strobogrammatic primes base 8 = 73, 262657, 295433, ... Strobogrammatic primes base 9 break the above pattern, as they can have the digit 8 and are A068188 (tetradic primes). Strobogrammatic primes base 10 == A007597. Except sometimes for the first element, these (for the same range of k) must all have an odd number of digits.
%F A155801 A000040 INTERSECTION A155584[1 < k < 11, n].
%e A155801 5189 = 1101011 (base 6) which numeral string is the same upside-down (and backwards). 11, 101, 181 and 619 are strobogrammatic base 10, the conventional interpretation of the word.
%Y A155801 Cf. A000040, A006995, A016041, A056130, A007597, A133207, A155584.
%K A155801 base,nonn
%O A155801 1,1
%A A155801 _Jonathan Vos Post_, Jan 27 2009