A260858 - OEIS

%I #10 Jun 29 2019 11:26:42

%S 0,1,81,5329,342225,21911761,1402427601,89755965649,45954960939217,

%T 188231512819194065,770996276517410920657,3158000748616424634669265,

%U 12935171066332946781853145297,52982460687699754593548358342865,217016158976818195107979529799293137

%N Base-8 representation of a(n) is the concatenation of the base-8 representations of 1, 2, ..., n, n-1, ..., 1.

%C Base-8 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.

%C The base 8 is not listed in A260343, because a(8) = A260851(8) = 45954960939217 is not prime and therefore not in A260852. See these sequences for more information.

%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 = 8, 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) = 81 = (8+1)^2 = 8^2 + 2*8 + 1 = 121_8, the concatenation of (1, 2, 1).

%e a(9) = 12345671011107654321_8, concatenation of (1, 2, 3, 4, 5, 6, 7, 10, 11, 10, 7, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base-8 representations of 8, 9, 8.

%o (PARI) a(n,b=8)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))

%K nonn,base

%O 0,3

%A _M. F. Hasler_, Aug 01 2015