

A166623


Irregular triangle read by rows, in which row n lists the Munchhausen numbers in base n, for 2 <= n.


3



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
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OFFSET

2,2


COMMENTS

Let N = Sum_i d_i b^i be the base b expansion of N. Then N has the Munchausen 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)
Daan van Berkel, On a curious property of 3435 [From Daan van Berkel (daan.v.berkel.1980(AT)gmail.com), Nov 17 2009]


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 Munchausen 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;


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



