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A220120 Bases having a record-sized smallest prime such that there are two smaller primes with which all 6 ways of juxtaposition in the base are prime. 1

%I

%S 2,7,12,18,20,24,26,29,41,53,72,107,137,152,158,314,1007,1097,1763

%N Bases having a record-sized smallest prime such that there are two smaller primes with which all 6 ways of juxtaposition in the base are prime.

%C Ties occur with bases 13 and 1553, which are detailed in the EXAMPLE section for completeness. See A220121 for the rest of the data.

%e In base 13, for any triple of primes under 103--the record corresponding to a(3)=12--at least 1 of the ways of stringing the primes together gives a composite; but {11,73,103} is a set giving primes all 6 ways: In base 13, these 3 primes are written B, 58 and 7C; and {587CB, 58B7C, 7C58B, 7CB58, B587C, B7C58} in base 13 corresponds to decimal {161731, 162343, 227251, 228223, 326611, 331651} (all of which are prime).

%e Base 1553 also ties the record set by base a(18)=1097, with no triple of primes under 1061 giving just primes, while the triple {197, 911, 1061} does.

%Y Cf. A220121.

%K nonn,base

%O 1,1

%A _James G. Merickel_, Dec 05 2012

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