

A260853


Base3 representation of a(n) is the concatenation of the base3 representations of 1, 2, ..., n, n1, ..., 1.


20



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

0,3


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.


LINKS

Table of n, a(n) for n=0..15.
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) = 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 base3 representation of 3.


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 *)


PROG

(PARI) a(n, b=3)=sum(i=1, #n=concat(vector(n*21, k, digits(min(k, n*2k), b))), n[i]*b^(#ni))


CROSSREFS

Base3 variant of A173426 (base 10) and A173427 (base 2). See A260854  A260866 for variants in other bases b = 4, ..., 16.
Sequence in context: A223686 A000489 A075852 * A068792 A229583 A241077
Adjacent sequences: A260850 A260851 A260852 * A260854 A260855 A260856


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Aug 01 2015


STATUS

approved



