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 A243025 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). 2
 1, 4155, 4355, 1953504, 1954329, 522169982 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Subset of A243023. This sequence is finite by using the same argument that Armstrong numbers (A005188) are finite. - Robert G. Wilson v, Jun 01 2014 LINKS EXAMPLE 1^1 = 1. 5^5 + 5^1 + 1^4 + 4^5 = 4155. 5^5 + 5^3 + 3^4 + 4^5 = 4355. 4^0 + 0^5 + 5^3 + 3^5 + 5^9 + 9^1 + 1^4 = 1953504. 9^2 + 2^3 + 3^4 + 4^5 + 5^9 + 9^1 + 1^9 = 1954329. MAPLE with(numtheory): P:=proc(q) local a, b, k, ok, n; for n from 10 to q do a:=[]; b:=n; 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) do if a[k-1]=0 and a[k]=0 then ok:=0; break; else b:=b+a[k-1]^a[k]; fi; od; if ok=1 then if n=(b+a[nops(a)]^a[nops(1)]) then print(n); fi; fi; od; end: P(10^10); MATHEMATICA 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 *) CROSSREFS Cf. A243023, A243024. Cf. A005188, A003321. Sequence in context: A052464 A161752 A145205 * A196494 A104824 A168663 Adjacent sequences:  A243022 A243023 A243024 * A243026 A243027 A243028 KEYWORD nonn,base,fini,full AUTHOR Paolo P. Lava, May 29 2014 EXTENSIONS Added a(1) as 1 and a(6) by Robert G. Wilson v, Jun 01 2014 STATUS approved

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Last modified June 4 03:40 EDT 2020. Contains 334815 sequences. (Running on oeis4.)