A083971 Reverse of k concatenated with k, divided by k, where k = A083970(n).
11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 101, 176, 341, 451, 11, 101, 176, 209, 11, 101, 176, 11, 101, 121, 176, 11, 101, 11, 101, 11, 77, 101, 11, 101, 11, 101, 11, 1001, 101, 1001, 176, 1001, 4169, 1001, 1751, 1001, 341, 1001, 1001, 3401, 5126, 1001, 451, 1001, 1001, 4501, 11, 1001, 1001
Offset: 1
Links
- Robert Israel, Table of n, a(n) for n = 1..10000
Programs
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Maple
f:= proc(n) local L,m,i,v; L:= convert(n,base,10); m:= nops(L); v:= add(10^(2*m-i)*L[i],i=1..m)/n+1; if v::integer then v else NULL fi end proc: map(f, [$1..1000]); # Robert Israel, Jul 26 2015 -
Mathematica
A083970 = Select[ Range[ 250 ], Divisible[ FromDigits[ Flatten[ { Reverse[ IntegerDigits[ # ] ], IntegerDigits[ # ] } ] ], # ] & ]; Table[ FromDigits[ Flatten[ { Reverse[ IntegerDigits[ tmp ] ], IntegerDigits[ tmp ] } ] ] / tmp, {tmp, A083970} ] (* Kevin Southwick, Jul 26 2015 *)
Formula
Note that when n is a palindrome, R(n)=n, so R(n) concat n = (10^d)n + n, where d is the number of digits of n, and R(n) is the reverse of n. Dividing by n, we obtain (R(n) concat n)/n = 10^d + 1. - Sam Alexander, Oct 21 2003; edited by Kevin Southwick, Jul 26 2015
Extensions
Corrected and extended by Sam Alexander, Oct 21 2003
Name edited by Charles R Greathouse IV, Aug 05 2015