A101335 Let n = d_1 d_2 ... d_k in base 10 and f(n) = Sum_{i=1..k} d_i^k; sequence gives numbers n such that n != f(n) but n = f(f(n)).

136, 244, 2178, 6514, 58618, 76438, 2755907, 6586433, 8139850, 9057586, 277668893, 756738746, 21914086555935085, 37878721692554416, 187864919457180831, 375609204308055082, 13397885590701080090, 40091536165423401387, 108493282045082839040458, 183144838903847612823687

Offset: 1

Author

Allyson A. Wilson (Foxtail(AT)southwind.net), May 04 2005

Keywords

• nonn
• base
• fini

Examples

			136 => 1^3+3^3+6^3=244 => 2^3+4^3+4^3=136.
2178 => 2^4+1^4+7^4+8^4=6514 => 6^4+5^4+1^4+4^4=2178.
		

References

• Ken Follett, Code to Zero, Dutton, NY 2000, p. 84.

Links

• Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..32

Crossrefs

Cf. A005188.

Subsequence of A157714.

Programs

Mathematica

f[n_] := Plus @@ (IntegerDigits[n]^Floor[Log[10, n] + 1]); Do[ lst = NestList[f, n, 2]; If[lst[[1]] == lst[[3]] != lst[[2]], Print[n]], {n, 110000000}] (* Robert G. Wilson v, May 21 2005 *)

Extensions

a(11)-a(20) from Tim Johannes Ohrtmann, Aug 27 2015