|
%I #18 Jun 29 2019 11:23:38
%S 0,1,25,441,27961,7148857,1830131001,468514084153,119939614479673,
%T 30704541449950521,7860362613477971257,2012252829087011018041,
%U 515136724246861226808633,131875001407205856562222393,33760000360244849399916500281,8642560092222683848298425324857
%N Base-4 representation of a(n) is the concatenation of the base-4 representations of 1, 2, ..., n, n-1, ..., 1.
%C The base 4 is listed in A260343, which means that a(4) = A260851(4) = 27961 is prime and therefore 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
%e a(0) = 0 is the result of the empty sum corresponding to 0 digits.
%e a(2) = 25 = 16 + 2*4 + 1 = 121_4 is the concatenation of (1, 2, 1).
%e a(4) = 27961 = 12310321_4 is the concatenation of (1, 2, 3, 10, 3, 2, 1), where the middle "10" is the base-4 representation of 4.
%o (PARI) a(n,b=4)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))
%Y Base-4 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
|
