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 A074481 Triangle T(p,k) read by rows, where p runs through the primes and 1 <= k <= p-1. T(p,k) = 1 if the reverse of the base-k expansion of p is a prime, otherwise 0. 1

%I

%S 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,

%T 1,1,1,0,1,1,0,1,0,1,1,1,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,

%U 1,1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,1,1,1,1,1,0,1,1,0,1,1,0,0,1,0,1,0

%N Triangle T(p,k) read by rows, where p runs through the primes and 1 <= k <= p-1. T(p,k) = 1 if the reverse of the base-k expansion of p is a prime, otherwise 0.

%C Row p has p-1 terms.

%C A very large version of this pyramid, with 1's replaced with white dots and 0's replaced with black dots, shows a very interesting pattern (see link). The author says: "These primes form a pattern similar to an astronomical radiant (the point in the sky from which a meteor shower appears to originate)".

%e Writing 11 in bases 1 through 10, we obtain

%e 11111111111,1011,102,23,21,15,14,13,12,11. Reversing these, we obtain

%e 11111111111,1101,201,32,12,51,41,31,21,11. Now 32 (base 4) and 31 (octal) are composite, all others are prime, so the row for 11 reads.

%e 1,1,1,0,1,1,1,0,1,1

%e Triangle begins:

%e .1

%e .1 1

%e .1 1 1 1

%e .1 1 1 1 1 1

%e .1 1 1 0 1 1 1 0 1 1

%e ....

%Y See A089829 for another version.

%K base,easy,nonn,tabf

%O 2,1