

A260863


Base13 representation of a(n) is the concatenation of the base13 representations of 1, 2, ..., n, n1, ..., 1.


1



0, 1, 196, 33489, 5664400, 957345481, 161792190756, 27342890695849, 4620948663553600, 780940325907974961, 131978915101424183716, 22304436652439380447009, 3769449794266138309731600, 8281481197999449959084458465, 236527384496061684935031509169004
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OFFSET

0,3


COMMENTS

See A260343 for the bases b such that A260851(b) = A_b(b) = b*c + (c  b)*(1 + b*c), is prime, where A_b is the baseb sequence, as here with b = 13, and c = R(b,b) = (b^n1)/(b1) is the baseb repunit of length b.


LINKS

Table of n, a(n) for n=0..14.
D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015


FORMULA

For n < b = 13, we have a(n) = A_b(n) = R(b,n)^2, where R(b,n) = (b^n1)/(b1) are the baseb repunits.


EXAMPLE

a(0) = 0 is the result of the empty sum corresponding to 0 digits.
a(2) = (13+1)^2 = 13^2 + 2*13 + 1 = 121_13, concatenation of (1, 2, 1).
a(14) = 123456789abc101110cba987654321_13 is the concatenation of (1, 2, 3, ..., 9, a, b, c, 10, 11, 10, c, ..., 1), where "c, 10, 11" are the base13 representations of 12, 13, 14.


PROG

(PARI) a(n, b=13)=sum(i=1, #n=concat(vector(n*21, k, digits(min(k, n*2k), b))), n[i]*b^(#ni))


CROSSREFS

Base13 variant of A173426 (base 10) and A173427 (base 2). See A260853  A260866 for variants in other bases.
Sequence in context: A076002 A145020 A333641 * A013755 A071410 A013871
Adjacent sequences: A260860 A260861 A260862 * A260864 A260865 A260866


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Aug 01 2015


STATUS

approved



