A046253 Equal to the sum of its nonzero digits raised to its own power.

0, 1, 3435, 438579088

Offset: 1

Author

Patrick De Geest, May 15 1998

Keywords

• nonn
• fini
• full
• base

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

Examples

			3435 = 3^3 + 4^4 + 3^3 + 5^5.
		

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.
• Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 37.
• 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.

Crossrefs

Cf. A032799, A166623.

Fixed points of A045512. See also A045503 (includes zero digits).

Programs

C

see Bailey and Hutchens links

Mathematica

Select[Range[0,10000],Total[#^#&/@DeleteCases[IntegerDigits@#,0]]==#&]  (* Giorgos Kalogeropoulos, May 08 2019 *)

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