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A260852 Primes in A260851: numbers whose base n expansion is equal to the concatenation of the base n expansions of (1, 2, 3, ..., n-1, n, n-1, ..., 3, 2, 1).

%I A260852 #24 Feb 19 2023 16:29:58
%S A260852 13,439,27961,522134761,21107054541321649,12345678910987654321,
%T A260852 24197857203266734883076090685781525281
%N A260852 Primes in A260851: numbers whose base n expansion is equal to the concatenation of the base n expansions of (1, 2, 3, ..., n-1, n, n-1, ..., 3, 2, 1).
%C A260852 Primes of the form (1+r(b)*b)*(r(b)-b+1)-1 with r(b)=(b^b-1)/(b-1).
%C A260852 Sequences A173427, A260853 - A260859, A173426, A260861 - A260866, A260860 list the numbers whose base b expansion is the concatenation of the base b expansions of (1, 2, ..., n, n-1, ..., 1). For n < b these are the squares of the repdigits of length n in base b, so the first candidate is the b-th term. These are the numbers listed in A260851. For the bases listed in A260343, this candidate is indeed prime: these are the primes listed here.
%C A260852 a(8) = A260851(40) has already 127 digits and is therefore too large to be displayed here.
%H A260852 D. Broadhurst, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;a39bf149.1002">Primes from concatenation: results and heuristics</a>, NmbrThry List, August 1, 2015
%H A260852 <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>
%F A260852 a(n) = A260851(A260343(n)).
%o A260852 (PARI) for(b=2,999,ispseudoprime(p=(1+b*c=(b^b-1)\(b-1))*(c-b+1)-1)&&print1(p","))
%Y A260852 Cf. A173427, A260853 - A260859, A173426, A260861 - A260866, A260860, A260851.
%K A260852 nonn,base
%O A260852 1,1
%A A260852 _M. F. Hasler_, Aug 02 2015