

A260858


Base8 representation of a(n) is the concatenation of the base8 representations of 1, 2, ..., n, n1, ..., 1.


1



0, 1, 81, 5329, 342225, 21911761, 1402427601, 89755965649, 45954960939217, 188231512819194065, 770996276517410920657, 3158000748616424634669265, 12935171066332946781853145297, 52982460687699754593548358342865, 217016158976818195107979529799293137
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OFFSET

0,3


COMMENTS

Base8 variant of A173426 (base 10) and A173427 (base 2). See A260853  A260866 for variants in other bases.
The base 8 is not listed in A260343, because a(8) = A260851(8) = 45954960939217 is not prime and therefore not in A260852. See these sequences for more information.


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 = 8, 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) = 81 = (8+1)^2 = 8^2 + 2*8 + 1 = 121_8, the concatenation of (1, 2, 1).
a(9) = 12345671011107654321_8, concatenation of (1, 2, 3, 4, 5, 6, 7, 10, 11, 10, 7, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base8 representations of 8, 9, 8.


PROG

(PARI) a(n, b=8)=sum(i=1, #n=concat(vector(n*21, k, digits(min(k, n*2k), b))), n[i]*b^(#ni))


CROSSREFS

Sequence in context: A187454 A206406 A238172 * A237300 A237937 A060349
Adjacent sequences: A260855 A260856 A260857 * A260859 A260860 A260861


KEYWORD

nonn,base


AUTHOR

M. F. Hasler, Aug 01 2015


STATUS

approved



