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.

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

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..19.

Example

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).
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.

Crossrefs

Cf. A220121.

Sequence in context: A105501 A016873 A019592 * A131190 A099353 A297432

Adjacent sequences: A220117 A220118 A220119 * A220121 A220122 A220123

Keyword

nonn,base

Author

James G. Merickel, Dec 05 2012

Status

approved