A243025 - OEIS

%I #16 Sep 29 2014 11:12:09

%S 1,4155,4355,1953504,1954329,522169982

%N Fixed points of the transform n = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + ... + d_(2)*10 + d_(1) -> Sum_{i=1..k-1}{d_(i)^d(i+1)}+d(k)^d(1) (A243023).

%C Subset of A243023.

%C This sequence is finite by using the same argument that Armstrong numbers (A005188) are finite. - _Robert G. Wilson v_, Jun 01 2014

%e 1^1 = 1.

%e 5^5 + 5^1 + 1^4 + 4^5 = 4155.

%e 5^5 + 5^3 + 3^4 + 4^5 = 4355.

%e 4^0 + 0^5 + 5^3 + 3^5 + 5^9 + 9^1 + 1^4 = 1953504.

%e 9^2 + 2^3 + 3^4 + 4^5 + 5^9 + 9^1 + 1^9 = 1954329.

%p with(numtheory): P:=proc(q) local a,b,k,ok,n; for n from 10 to q do a:=[]; b:=n;

%p while b>0 do a:=[op(a),b mod 10]; b:=trunc(b/10); od; b:=0; ok:=1; for k from 2 to nops(a)

%p do if a[k-1]=0 and a[k]=0 then ok:=0; break; else b:=b+a[k-1]^a[k]; fi; od;

%p if ok=1 then if n=(b+a[nops(a)]^a[nops(1)]) then print(n);

%p fi; fi; od; end: P(10^10);

%t fQ[n_] := Block[{r = Reverse@ IntegerDigits@ n}, n == Plus @@ (r^RotateLeft@ r)]; k = 1; lst = {}; While[k < 1000000001, If[ fQ@ k, AppendTo[ lst, k]; Print@ k]; k++] (* _Robert G. Wilson v_, Jun 01 2014 *)

%Y Cf. A243023, A243024.

%Y Cf. A005188, A003321.

%K nonn,base,fini,full

%O 1,2

%A _Paolo P. Lava_, May 29 2014

%E Added a(1) as 1 and a(6) by _Robert G. Wilson v_, Jun 01 2014