

A155801


Nontrivial "Strobogrammatic" primes, the same "upsidedown" in at least one base b with 2 <= b <= 10.


0



3, 5, 7, 11, 13, 17, 31, 37, 43, 73, 101, 107, 127, 181, 257, 313, 443, 619, 757, 1093, 1193, 1297, 1453, 1571, 1619, 1787, 1831, 1879, 2801, 4889, 5113, 5189, 5557, 5869, 5981, 6211, 6827, 7607, 7759, 7919, 8191
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

I have to say "nontrivial" because every nonnegative integer is strobogrammatic base 1. Strobogrammatic binary primes == primes in A006995 == A016041. Strobogrammatic primes base 3 = 13, 757, 1093, 9103, ... == primes strobogrammatic in bases 2 and 3. For bases 2 < k < 8 we have that every strobogrammatic prime base k must also be strobogrammatic base 2 and hence palindromatic base 2. Hence we have, for example, strobogrammatic base 4 primes = A056130 = "Palindromic primes in bases 2 and 4."
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 the 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.


LINKS

Table of n, a(n) for n=1..41.


FORMULA

A000040 INTERSECTION A155584[1<k<11,n].


EXAMPLE

5189 = 1101011 (base 6) which numeral string is the same upsidedown (and backwards). 11, 101, 181 and 619 are strobogrammatic base 10, the conventional interpretetation of the word.


CROSSREFS

Cf. A000040, A006995, A016041, A056130, A007597, A133207, A155584.
Sequence in context: A106284 A126145 A206864 * A228118 A136186 A023210
Adjacent sequences: A155798 A155799 A155800 * A155802 A155803 A155804


KEYWORD

base,nonn


AUTHOR

Jonathan Vos Post, Jan 27 2009


STATUS

approved



