A260856 - OEIS

%I #13 Sep 10 2018 15:08:11

%S 0,1,49,1849,67081,2418025,522134761,676678989289,876975982612969,

%T 1136560874204496361,1472982892995886760425,1908985829323636470956521,

%U 2474045634803467686907986409,3206363142705295375772778742249,4155446632946062852128962559066601

%N Base-6 representation is the concatenation of the base-6 representations of 1, 2, ..., n, n-1, ..., 1.

%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

%e a(0) = 0 is the result of the empty sum corresponding to 0 digits.

%e a(2) = 49 = (6+1)^2 = 6^2 + 2*6 + 1 = 121_6 is the concatenation of (1, 2, 1).

%e a(7) = 676678989289 = 1234510111054321_6 is the concatenation of (1, 2, 3, 4, 5, 10, 11, 10, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base 6 representations of 6, 7, 6.

%o (PARI) a(n,b=6)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))

%Y Base 6 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for variants in other bases b = 3, ..., 16.

%K nonn,base

%O 0,3

%A _M. F. Hasler_, Aug 01 2015