A260856 Base-6 representation is the concatenation of the base-6 representations of 1, 2, ..., n, n-1, ..., 1.

0, 1, 49, 1849, 67081, 2418025, 522134761, 676678989289, 876975982612969, 1136560874204496361, 1472982892995886760425, 1908985829323636470956521, 2474045634803467686907986409, 3206363142705295375772778742249, 4155446632946062852128962559066601

Offset

0,3

Links

Table of n, a(n) for n=0..14.

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

Example

a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = 49 = (6+1)^2 = 6^2 + 2*6 + 1 = 121_6 is the concatenation of (1, 2, 1).
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.

Prog

(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))

Crossrefs

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

Sequence in context: A008843 A145848 A014942 * A367378 A065785 A163927

Adjacent sequences: A260853 A260854 A260855 * A260857 A260858 A260859

Keyword

nonn,base

Author

M. F. Hasler, Aug 01 2015

Status

approved