

A260861


Base11 representation of a(n) is the concatenation of the base11 representations of 1, 2, ..., n, n1, ..., 1.


6



0, 1, 144, 17689, 2143296, 259371025, 31384248336, 3797497946089, 459497294348544, 55599173087763361, 6727499948806851600, 8954302429379707945271, 131099941868210323821706774, 1919434248892467772593071038679, 28102436838034620750856132266604106
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OFFSET

0,3


COMMENTS

The first prime in this sequence is a(13) = A260871(9). Since a(11) is not prime, the base 11 is not listed in A260343.


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 = 11, we have a(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) = (11+1)^2 = 11^2 + 2*11 + 1 = 121_11, concatenation of (1, 2, 1).
a(12) = 123456789a101110a987654321_11 is the concatenation of (1, 2, 3, ..., 9, a, 10, 11, 10, a, 9, ..., 1), where "a, 10, 11" are the base11 representations of 10, 11, 12.


PROG

(PARI) a(n, b=11)=sum(i=1, #n=concat(vector(n*21, k, digits(min(k, n*2k), b))), n[i]*b^(#ni))


CROSSREFS

Base11 variant of A173426 (base 10) and A173427 (base 2). See A260853  A260866 for variants in other bases.
Sequence in context: A252779 A238284 A249181 * A079658 A280024 A091037
Adjacent sequences: A260858 A260859 A260860 * A260862 A260863 A260864


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Aug 01 2015


STATUS

approved



