%I #19 Jun 29 2019 11:27:25
%S 0,1,289,74529,19088161,4886709025,1250999747361,320255971115809,
%T 81985529178309409,20988295478809805601,5373003642721911784225,
%U 1375488932539155041567521,352125166730061220638180129,90144042682896272963324429089,23076874926821455486290258903841
%N Base-16 representation of a(n) is the concatenation of the base-16 representations of 1, 2, ..., n, n-1, ..., 1.
%C See A260343 for the bases b such that B(b) = A_b(b) = b*c + (c - b)*(1 + b*c), is prime, where A_b is the base-b sequence, as here with b=16, and c = R(b,b) = (b^n-1)/(b-1) is the base-b repunit of length b.
%H D. Broadhurst, <a href="https://listserv.nodak.edu/cgi-bin/wa.exe?A2=NMBRTHRY;af419558.1508">Primes from concatenation: results and heuristics</a>, NmbrThry List, August 1, 2015
%F For n < b = 16, we have a(n) = A_b(n) = R(b,n)^2, where R(b,n) = (b^n-1)/(b-1) are the base-b repunits.
%e a(0) = 0 is the result of the empty sum corresponding to 0 digits.
%e a(2) = (16+1)^2 = 16^2 + 2*16 + 1 = 121_16, concatenation of (1, 2, 1).
%e a(17) = 123456789abcdef101110fedcba987654321_16 is the concatenation of (1, 2, 3, ..., 9, a, ..., f, 10, 11, 10, f, e, ..., 1), where the middle "10, 11, 10" are the base-16 representations of 16, 17, 16.
%o (PARI) a(n,b=16)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))
%Y Base-16 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260865 for variants in other bases.
%K nonn,base
%O 0,3
%A _M. F. Hasler_, Aug 01 2015