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 A287076 a(n) = least k > n with the same sum of digits as n in some base b > 1. 1
 2, 4, 5, 6, 6, 9, 10, 12, 10, 12, 13, 16, 14, 16, 19, 20, 18, 20, 21, 22, 22, 24, 25, 30, 26, 28, 29, 30, 30, 36, 33, 34, 34, 36, 37, 40, 38, 40, 42, 42, 42, 44, 45, 48, 46, 48, 49, 56, 50, 52, 53, 56, 54, 57, 57, 58, 58, 60, 61, 64, 62, 66, 67, 66, 66, 68, 69 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS More formally: a(n) = Min_{b>1} f_b(n), where f_b(n) = least k > n with the same sum of digits as n in base b. We have the following properties: - f_b(b) = b^2 for any b > 1, - f_b(b^k) = b^(k+1) for any b > 1 and k >= 0, - f_b(n) = b + n - 1 for any b > 1 and n < b, - f_b(n) - n >= b - 1 for any b > 1 and n > 0. Also, f_2 = A057168 and f_10 = A228915. For any n > 0, n < a(n) <= 2*n. Conjecturally, a(n) ~ n. The derived sequence e(n) = a(n) - n is unbounded: for any n > 0: - for any b such that 1 < b <= n, let x_b = the least power of b such that f_b(i*x_b) - i*x_b >= n for any i > 0, - let X = Lcm_{b=2..n} x_b, - then f_b(X) - X >= n for any b such that 1 < b <= n, - also, f_b(X) - X >= b - 1 >= n for any b > n, - hence a(X) - X = e(X) >= n, QED. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..10000 Rémy Sigrist, PARI program for A287076 EXAMPLE The following table shows f_b(8) for all bases b > 1: b    f_b(8)   8 in base b   f_b(8) in base b --   ------   -----------   ---------------- 2        16        "1000"            "10000" 3        14          "22"              "112" 4        17          "20"              "101" 5        12          "13"               "22" 6        13          "12"               "21" 7        14          "11"               "20" 8        64          "10"              "100" b>8     b+7           "8"               "17" Hence, a(8) = f_5(8) = 12. CROSSREFS Cf. A057168, A228915. Sequence in context: A083788 A058317 A278761 * A344587 A100006 A196262 Adjacent sequences:  A287073 A287074 A287075 * A287077 A287078 A287079 KEYWORD nonn,base AUTHOR Rémy Sigrist, May 19 2017 STATUS approved

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Last modified December 1 20:25 EST 2021. Contains 349435 sequences. (Running on oeis4.)