A285463 Primes palindromic in base 8 that are the sum of 3 consecutive primes, the middle one palindromic in base 8.

349, 936227, 241853952611, 248296403939, 402089961397, 14290027171787, 22798543031501, 25498249343221, 928194481893587, 1108961833390907, 56735483914668107, 56840981804535371, 65947215239750827, 67113509914884011, 90309903454333957, 97912610367958237, 99307055366487077

Offset

1,1

Comments

Base 8 variant of A113846.

Similar arguments as for A113846 can be used to show that for all terms the first (and last) digit in base 8 is either 3 or 5.

All terms so far seem to follow one of the following patterns in base 8:

3w3, where w is an odd-length word consisting of the digits 2 and 5 only or of the digits 1, 4, 7 only.

abwba, where a is either 3 or 5, b is either the empty word or a single digit from 0 to 7 and w is an odd-length word consisting of the digits 0, 3, 6 only or of the digits 1, 4, 7 only.

By searching only through these patterns, much larger terms were found such as 473953150492647002336509521341 = 576666333366030333030663333666675_3.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..35

Chai Wah Wu, List of terms that are of the form 3w3 or abwba in base 8 (see comments for definitions)

Crossrefs

Cf. A113846.

Sequence in context: A031420 A273530 A282341 * A138944 A043619 A249430

Adjacent sequences: A285460 A285461 A285462 * A285464 A285465 A285466

Keyword

nonn,base,hard

Author

Chai Wah Wu, Apr 21 2017

Status

approved