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A046253
Equal to the sum of its nonzero digits raised to its own power.
8
0, 1, 3435, 438579088
OFFSET
1,3
COMMENTS
A variant of Münchausen numbers, cf. A166623.
The sequence is finite, because the sum can't exceed 9^9*L < 10^9*L, where L is the number of digits, and for L > 10 this is less than the number N >= 10^(L-1). - M. F. Hasler, Oct 01 2024
REFERENCES
J. S. Madachy, "Madachy's Mathematical Recreations", Dover N.Y., pp. 163-175.
C. A. Pickover, "Keys to Infinity", Wiley 1995, Ch. 22, pp. 169-171.
David Wells, "Curious and Interesting Numbers", Penguin 1988, pp. 169, 190.
LINKS
Devin Akman, Munchausen Numbers Redux, Missouri J. Math. Sci. 30 (2018), no. 1, 1--4.
Geoff Bailey, C program for the sequence (cf. Hutchens link for more info), Aug. 1998.
Daan van Berkel, On a curious property of 3435, arXiv:0911.3038 [math.HO], 2009.
Jason Hutchens, power summation (originally at ciips.ee.uwa.edu.au/~hutch), 1997.
Eric Weisstein's World of Mathematics, Münchhausen Number.
EXAMPLE
3435 = 3^3 + 4^4 + 3^3 + 5^5.
MATHEMATICA
Select[Range[0, 10000], Total[#^#&/@DeleteCases[IntegerDigits@#, 0]]==#&] (* Giorgos Kalogeropoulos, May 08 2019 *)
PROG
(C) see Bailey and Hutchens links
(PARI) select( {is_A046253(n)=n==A045512(n)}, [0..10^4]) \\ To find the 4th solution, multiply the set by 51817. - M. F. Hasler, Oct 01 2024
CROSSREFS
Fixed points of A045512. See also A045503 (includes zero digits).
Sequence in context: A172708 A244170 A245792 * A031824 A254093 A254086
KEYWORD
nonn,fini,full,base
AUTHOR
Patrick De Geest, May 15 1998
STATUS
approved