A260853 Base-3 representation of a(n) is the concatenation of the base-3 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 16, 439, 35350, 2864599, 232046890, 18795930559, 1522471570630, 369960528437035, 269701223137448146, 196612191672080116867, 143330287729139571972130, 104487779754548024866115515, 76171591441065652665051372946, 55529090160536864641400481743827

Offset: 0

Author

M. F. Hasler, Aug 01 2015

Keywords

• nonn
• base

Comments

The base 3 is listed in A260343, which means that a(3) = A260851(3) = 439 = 121021_3 is prime and therefore in A260852. See these sequences for more information.

Examples

			a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = 16 = 121_3 is the concatenation of (1, 2, 1).
a(3) = 439 = 121021_3 is the concatenation of (1, 2, 10, 2, 1), where the middle "10" is the base-3 representation of 3.
		

Links

• D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Base-3 variant of A173426 (base 10) and A173427 (base 2). See A260854 - A260866 for variants in other bases b = 4, ..., 16.

Programs

Mathematica

Join[{0},Table[FromDigits[Join[Flatten[IntegerDigits[Range[n], 3]], Flatten[ Reverse[ Most[ IntegerDigits[Range[n],3]]]]],3],{n,20}]] (* Harvey P. Dale, Mar 11 2019 *)

PARI

a(n,b=3)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))