A260859 Base-9 representation of a(n) is the concatenation of the base-9 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 100, 8281, 672400, 54479161, 4412944900, 357449732641, 28953439105600, 21107054541321649, 138483384602892402628, 908589486379899193778809, 5961255620138564686107812272, 39111798123729126657669459066697, 256612507489786800304910707633347364

Offset: 0

Author

M. F. Hasler, Aug 01 2015

Keywords

• nonn
• base

Comments

The base 9 is listed in A260343, because a(9) = A260851(9) = 21107054541321649 = 123456781087654321_9 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) = 100 = (9+1)^2 = 9^2 + 2*9 + 1 = 121_9, concatenation of (1, 2, 1).
a(10) = 1234567810111087654321_9 is the concatenation of (1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 10, 8, 7, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base-9 representations of 9, 10, 9.
		

Links

• D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015

Crossrefs

Base-9 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for the variants in other bases.

Programs

PARI

a(n,b=9)=sum(i=1,#n=concat(vector(n*2-1,k,digits(min(k,n*2-k),b))),n[i]*b^(#n-i))

Formula

For n < b = 9, 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.