

A260864


Base14 representation of a(n) is the concatenation of the base14 representations of 1, 2, ..., n, n1, ..., 1.


2



0, 1, 225, 44521, 8732025, 1711559641, 335466848025, 65751518430361, 12887297839395225, 2525910379700086681, 495078434465717705625, 97035373155903680328601, 19018933138565843484771225, 3727710895159027432980276121, 10228838696316240496325238416281
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OFFSET

0,3


COMMENTS

See A260343 for the bases b such that A260851(b) = A_b(b) = b*r + (r  b)*(1 + b*r), is prime, where A_b is the baseb sequence, as here with b=14, and r = (b^b1)/(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 = 14, we have a(n) = R(14,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) = (14+1)^2 = 14^2 + 2*14 + 1 = 121_14, concatenation of (1, 2, 1).
a(15) = 123456789abcd101110dcba987654321_14 is the concatenation of (1, 2, 3, ..., 9, a, b, c, d, 10, 11, 10, d, ..., 1), where "d, 10, 11" are the base14 representations of 13, 14, 15.


PROG

(PARI) a(n, b=14)=sum(i=1, #n=concat(vector(n*21, k, digits(min(k, n*2k), b))), n[i]*b^(#ni))


CROSSREFS

Base14 variant of A173426 (base 10) and A173427 (base 2). See A260853  A260866 for variants in other bases.
For primes see A261408.
Sequence in context: A061051 A036428 A183822 * A265420 A171109 A239478
Adjacent sequences: A260861 A260862 A260863 * A260865 A260866 A260867


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Aug 01 2015


STATUS

approved



