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 A260859 Base-9 representation of a(n) is the concatenation of the base-9 representations of 1, 2, ..., n, n-1, ..., 1. 6
 0, 1, 100, 8281, 672400, 54479161, 4412944900, 357449732641, 28953439105600, 21107054541321649, 138483384602892402628, 908589486379899193778809, 5961255620138564686107812272, 39111798123729126657669459066697, 256612507489786800304910707633347364 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS The base 9 is listed in A260343, because a(9) = A260851(9) = 21107054541321649 = 123456781087654321_9 is prime and therefore in A260852. See these sequences for more information. LINKS D. Broadhurst, Primes from concatenation: results and heuristics, NmbrThry List, August 1, 2015 FORMULA For n < b = 9, we have a(n) = A_b(n) = R(b,n)^2, where R(b,n) = (b^n-1)/(b-1) are the base-b repunits. EXAMPLE a(0) = 0 is the result of the empty sum corresponding to 0 digits. a(2) = 100 = (9+1)^2 = 9^2 + 2*9 + 1 = 121_9, concatenation of (1, 2, 1). a(10) = 1234567810111087654321_9 is the concatenation of (1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 10, 8, 7, 6, 5, 4, 3, 2, 1), where the middle "10, 11, 10" are the base-9 representations of 9, 10, 9. PROG (PARI) a(n, b=9)=sum(i=1, #n=concat(vector(n*2-1, k, digits(min(k, n*2-k), b))), n[i]*b^(#n-i)) CROSSREFS Base-9 variant of A173426 (base 10) and A173427 (base 2). See A260853 - A260866 for the variants in other bases. Sequence in context: A245666 A210814 A065689 * A117687 A262806 A108741 Adjacent sequences:  A260856 A260857 A260858 * A260860 A260861 A260862 KEYWORD nonn,base AUTHOR M. F. Hasler, Aug 01 2015 STATUS approved

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Last modified November 22 18:55 EST 2019. Contains 329410 sequences. (Running on oeis4.)