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).
Original entry on oeis.org
1, 4155, 4355, 1953504, 1954329, 522169982
Offset: 1
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.
-
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);
-
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 *)
A243024
Consider a k-digit number m = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + ... + d_(2)*10 + d_(1). Sequence lists the numbers m that divide Sum_{i=1..k-1}{d_(i)^d_(i+1)}+d_(k)^d_(1).
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 9, 63, 448, 1899, 1942, 4155, 4355, 8503, 28375, 44569, 73687, 1953504, 1954329, 70860598, 522169982
Offset: 1
For 1899 we have: 9^9 + 9^8 + 8^1 + 1^9 = 430467219.
Finally 430467219/1899 = 226681.
For 1954329 we have: 9^2 + 2^3 +3^4 + 4^5 + 5^9 + 9^1 + 1^9 = 1954329.
-
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 type((b+a[nops(a)]^a[nops(1)])/n,integer) then print(n);
fi; fi; od; end: P(10^10);
-
isok(n) = d = digits(n); k = #d; (sum(i=1, k-1, j=k-i+1; d[j]^d[(j-1)])+ d[1]^d[k]) % n == 0; \\ Michel Marcus, Sep 29 2014
A243507
Consider a decimal number, n, with k digits. n = d(k)*10^(k-1) + d(k-1)*10^(k-2) + … + d(2)*10 + d_(1). Sequence lists the numbers n that divide s = Sum_{i=1..k} d(i)^d(i).
Original entry on oeis.org
1, 2, 3, 4, 5, 6, 7, 8, 9, 63, 64, 93, 377, 643, 699, 760, 2428, 3435, 13073, 46864, 184405, 208858, 1313290, 2326990, 2868720, 2868741, 18273988, 25265859, 33690905, 87889176, 194123725, 589957694
Offset: 1
63 is in the sequence because 6^6+3^3 = 46683 and 46683/63 = 741, an integer.
-
with(numtheory): P:=proc(q) local a,b,k,n; for n from 1 to q do a:=[]; b:=n; while b>0 do a:=[op(a),b mod 10]; b:=trunc(b/10); od; b:=0; for k from 1 to nops(a) do if a[k]=0 then b:=b+1; else b:=b+a[k]^a[k]; fi; od; if type(b/n,integer) then print(n); fi; od; end: P(10^10);
-
fQ[n_] := Block[{id = IntegerDigits@ n /. {0 -> 1}}, Mod[ Total[ id^id], n] == 0]; k = 1; lst = {}; While[k < 10000000001, If[ fQ@ k, AppendTo[ lst, k]; Print@ k]; k++]; lst
Showing 1-3 of 3 results.
Comments