login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Primes palindromic in base 8 that are the sum of 3 consecutive primes, the middle one palindromic in base 8.
1

%I #13 Apr 28 2017 03:18:45

%S 349,936227,241853952611,248296403939,402089961397,14290027171787,

%T 22798543031501,25498249343221,928194481893587,1108961833390907,

%U 56735483914668107,56840981804535371,65947215239750827,67113509914884011,90309903454333957,97912610367958237,99307055366487077

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

%C Base 8 variant of A113846.

%C 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.

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

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

%C 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.

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

%H Chai Wah Wu, <a href="/A285463/b285463.txt">Table of n, a(n) for n = 1..35</a>

%H Chai Wah Wu, <a href="/A285463/a285463.txt">List of terms that are of the form 3w3 or abwba in base 8 (see comments for definitions)</a>

%Y Cf. A113846.

%K nonn,base,hard

%O 1,1

%A _Chai Wah Wu_, Apr 21 2017