cp's OEIS Frontend

A260862 Base-12 representation of a(n) is the concatenation of the base-12 representations of 1, 2, ..., n, n-1, ..., 1.

%I A260862 #13 Jun 29 2019 11:26:54
%S A260862 0,1,169,24649,3553225,511709641,73686731209,10610895808969,
%T A260862 1527969074670025,220027547690625481,31683966878707771849,
%U A260862 4562491230669011577289,7883984846509322664831433,163482309777203435651765004745,3389969175540090458609916107975113
%N A260862 Base-12 representation of a(n) is the concatenation of the base-12 representations of 1, 2, ..., n, n-1, ..., 1.
%C A260862 The first prime in this sequence is a(16) = A260871(11). Since a(12) is not prime, the base 12 is not listed in A260343.
%H A260862 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 A260862 For n < b = 12, we have a(n) = R(b,n)^2, where R(b,n) = (b^n-1)/(b-1) are the base-b repunits.
%e A260862 a(0) = 0 is the result of the empty sum corresponding to 0 digits.
%e A260862 a(2) = (12+1)^2 = 12^2 + 2*12 + 1 = 121_12, concatenation of (1, 2, 1).
%e A260862 a(13) = 123456789ab101110ba987654321_12 is the concatenation of (1, 2, 3, ..., 9, a, b, 10, 11, 10, b, ..., 1), where "b, 10, 11" are the base-12 representations of 11, 12, 13.
%o A260862 (PARI) a(n,b=12)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))
%Y A260862 Base-12 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases.
%K A260862 nonn,base
%O A260862 0,3
%A A260862 _M. F. Hasler_, Aug 01 2015