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Right-truncatable, reversible primes in base 256.
11

%I #14 Mar 20 2014 21:04:41

%S 2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,

%T 97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,

%U 181,191,193,197,199,211,223,227,229,233,239,241,251,773,809,823

%N Right-truncatable, reversible primes in base 256.

%C See A238850 for definitions, and A238854 for comments on general context.

%C In base 256, there are 35127 such numbers (see A238855), shown here in decimal format. Base 256 is of interest to programmers because its digits correspond to 8-bit bytes and are easily readable in hexadecimal.

%H Stanislav Sykora, <a href="/A238853/b238853.txt">Table of n, a(n) for n = 1..35127</a>

%H Stanislav Sykora, <a href="https://oeis.org/wiki/File:GeneticThreads.txt">PARI/GP scripts for genetic threads</a>, with code and comments.

%e The largest such number is 143496996325262301365903209731563 which, written in hex format, with hyphens between bytes for better readability, is 07-13-2F-CD-51-E1-B1-11-EB-23-CD-B3-15-EB. Truncate on the right any number of bytes and the remaining prefix is still a prime, no matter whether the bytes are read from left to right, or vice versa!

%o (PARI) See the link.

%Y Cf. All in base 10: A238850, 16: A238851, 100: A238852.

%Y Cf. In base n: A238854 (largest), A238856 (maximum digits), A238857 (m-digits counts). Cf. A007500, A023107, A024770, A237600, A237601, A237602.

%K nonn,fini,full,base

%O 1,1

%A _Stanislav Sykora_, Mar 06 2014