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 A166623 Irregular triangle read by rows, in which row n lists the Münchhausen numbers in base n, for 2 <= n. 6
 1, 2, 1, 5, 8, 1, 29, 55, 1, 1, 3164, 3416, 1, 3665, 1, 1, 28, 96446, 923362, 1, 3435, 1, 34381388, 34381640, 1, 20017650854, 1, 93367, 30033648031, 8936504649405, 8936504649431, 1, 31, 93344, 17852200903304, 606046687989917 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS Let N = Sum_i d_i b^i be the base b expansion of N. Then N has the Münchhausen property in base b if and only if N = Sum_i (d_i)^(d_i). Convention: 0^0 = 1. LINKS Karl W. Heuer, Rows n = 2..35, flattened (each row starts with 1) John D. Cook, Münchausen numbers (2016) Daan van Berkel, On a curious property of 3435, arXiv:0911.3038 [math.HO], 2009. Eric W. Weisstein, "Münchhausen Number." From MathWorld--A Wolfram Web Resource. EXAMPLE For example: the base 4 representation of 29 is [1,3,1] (29 = 1*4^2 + 3*4^1 + 1*4^0). Furthermore, 29 = 1^1 + 3^3 + 1^1. Therefore 29 has the Münchhausen property in base 4. Because 1 = 1^1 in every base, a 1 in the sequence signifies a new base. So the sequence can best be read in the following form: 1, 2; 1, 5, 8; 1, 29, 55; 1; 1, 3164, 3416; 1, 3665; 1; 1, 28, 96446, 923362; 1, 3435; PROG (GAP) next := function(result, n) local i; result[1] := result[1] + 1; i := 1; while result[i] = n do result[i] := 0; i := i + 1; if (i <= Length(result)) then result[i] := result[i] + 1; else Add(result, 1); fi; od; return result; end; munchausen := function(coefficients) local sum, index; sum := 0; for index in coefficients do sum := sum + index^index; od; return sum; end; for m in [2..10] do max := 2*m^m; n := 1; coefficients := [1]; while n <= max do sum := munchausen(coefficients); if (n = sum) then Print(n, "\n"); fi; n := n + 1; coefficients := next(coefficients, m); od; od; (Python) from itertools import combinations_with_replacement from sympy.ntheory.factor_ import digits A166623_list = [] for b in range(2, 20):     sublist = []     for l in range(1, b+2):         for n in combinations_with_replacement(range(b), l):             x = sum(d**d for d in n)             if tuple(sorted(digits(x, b)[1:])) == n:                 sublist.append(x)     A166623_list.extend(sorted(sublist)) # Chai Wah Wu, May 20 2017 CROSSREFS See A046253 for base 10. Sequence in context: A193603 A059274 A082635 * A094510 A023677 A108599 Adjacent sequences:  A166620 A166621 A166622 * A166624 A166625 A166626 KEYWORD nonn,base,tabf AUTHOR Daan van Berkel (daan.v.berkel.1980(AT)gmail.com), Oct 18 2009 EXTENSIONS Edited (but not checked) by N. J. A. Sloane, Nov 10 2009 More terms from Karl W. Heuer, Aug 06 2011 STATUS approved

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Last modified October 21 13:24 EDT 2019. Contains 328299 sequences. (Running on oeis4.)