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 A366165 a(n) is the least k > 0 such that 10^(2*n-1) - k can be written as a product j*m, where j and m have an equal number of decimal digits. 2
 1, 1, 1, 1, 10, 1, 3, 1, 5, 3, 1, 6, 1, 7, 1, 2, 2, 1, 4, 7, 5, 1, 1, 3, 2, 1, 1, 1, 1, 2, 1, 1, 10, 4, 3, 3, 10, 1, 2, 3, 1, 1, 1, 7, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS a(n) <= 10 since 10^(2n-1)-10 = (10^(n-1)+1)(10^n-10). A consequence is that j and m in the product both have n decimal digits. - Chai Wah Wu, Oct 05 2023 LINKS Table of n, a(n) for n=1..46. EXAMPLE n a(n) 10^(2n-1)-a(n) j m 1 1 9 1 9 2 1 999 27 37 3 1 99999 123 813 4 1 9999999 2151 4649 5 10 999999990 10001 99990 6 1 99999999999 194841 513239 7 3 9999999999997 2769823 3610339 More than one pair (j,m) may exist, e.g., 9 = 1*9 = 3*3. PROG (PARI) a366165(n)={my (p10=10^(2*n-1)); for (dd=1, p10, my (d=p10-dd); fordiv (d, x, fordiv (d, y, if (x*y==d && #digits(x)==#digits(y), return(dd)))))}; (Python) from itertools import count, takewhile from sympy import divisors def A366165(n): a, l1, l2 = 10**((n<<1)-1), 10**(n-1), 10**n for k in count(1): b = a-k if any(l1<=db for d in takewhile(lambda m:m*m<=b, divisors(b))): return k # Chai Wah Wu, Oct 05 2023 CROSSREFS Cf. A002275, A003020, A004022, A057951, A327435. A067272 are the solutions for even exponents of 10, corresponding to (j,m) = (9,9), (99,99), (999,999), ... . Sequence in context: A359736 A010179 A174209 * A010181 A111525 A138261 Adjacent sequences: A366162 A366163 A366164 * A366166 A366167 A366168 KEYWORD nonn,base,more AUTHOR Hugo Pfoertner, Oct 04 2023 EXTENSIONS a(33)-a(35) from Chai Wah Wu, Oct 05 2023 a(36)-a(46) from Chai Wah Wu, Oct 07 2023 STATUS approved

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Last modified April 16 04:14 EDT 2024. Contains 371696 sequences. (Running on oeis4.)