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A071685 Non-palindromic numbers n, not divisible by 10, such that either n divides R(n) or R(n) divides n, where R(n) is the digit-reversal of n. 2
1089, 2178, 8712, 9801, 10989, 21978, 87912, 98901, 109989, 219978, 879912, 989901, 1099989, 2199978, 8799912, 9899901, 10891089, 10999989, 21782178, 21999978, 87128712, 87999912, 98019801, 98999901, 108901089, 109999989 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The quotient R(n)/n or n/R(n) is always 4 or 9.
This is the union of the four sequence A001232, A222814, A008918, A222815. Equivalently, the union of A008919 and A031877.
There are 4*Fibonacci(floor((n-2)/2)) terms with n digits (this is 2*A214927 or essentially 4*A103609). - Ray Chandler, Oct 12 2017
Conjecture: every term mod 100 is equal to 1, 12, 78, or 89. - Harvey P. Dale, Dec 13 2017
LINKS
N. J. A. Sloane, 2178 And All That, Fib. Quart., 52 (2014), 99-120.
FORMULA
x = q*R(x), q is integer q<>1, q<>10^j and neither of x or R(x) is divisible by 10.
EXAMPLE
Palindromic solutions like 12021 or also solutions divisible by 10 were filtered out like {8380,838; q=10} or {8400,48; q=175}. In case of m>R(m), q=m/R(m)=4 or 9.
MATHEMATICA
nd[x_, y_] := 10*x+y tn[x_] := Fold[nd, 0, x] ed[x_] := IntegerDigits[x] red[x_] := Reverse[IntegerDigits[x]] Do[s=Mod[Max[{n, tn[red[n]]}], Min[{n, r=tn[red[n]]}]]; If[Equal[s, 0]&&!Equal[Mod[n, 10], 0] &&!Equal[n, r], Print[{n, r/n}]], {n, 1, 1000000}]
npnQ[n_]:=Module[{r=IntegerReverse[n]}, !PalindromeQ[n]&&!Divisible[ n, 10] &&(Mod[n, r]==0||Mod[r, n]==0)]; Select[Range[11*10^7], npnQ] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 13 2017 *)
CROSSREFS
Sequence in context: A168661 A175698 A110819 * A008919 A110843 A354256
KEYWORD
base,easy,nonn
AUTHOR
Labos Elemer, Jun 03 2002
EXTENSIONS
Corrected and extended by Harvey P. Dale, Jul 01 2013
Edited by N. J. A. Sloane, Jul 02 2013
Missing terms inserted by Ray Chandler, Oct 09 2017
Incorrect comment removed by Ray Chandler, Oct 12 2017
STATUS
approved

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Last modified February 24 02:58 EST 2024. Contains 370288 sequences. (Running on oeis4.)