A072227 Numbers n such that reverse(d) divides reverse(n) for all divisors d of n.

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 13, 17, 19, 22, 23, 26, 27, 29, 31, 33, 37, 39, 41, 43, 44, 46, 47, 53, 55, 59, 61, 62, 66, 67, 69, 71, 73, 77, 79, 82, 83, 86, 88, 89, 93, 97, 99, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 143, 149, 151, 157, 163, 167, 169, 173

Offset

1,2

Comments

All primes are in this sequence, so a(n) << n log n. Does a(n) ~ n log n? That is, are composites of relative density 0 in this sequence? - Charles R Greathouse IV, Sep 12 2012

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

The divisors of 187 are 1, 11, 17, 187, with reverses 1, 11, 71, 781 which all divide 781, the reverse of 187, so 187 is a term of the sequence.

Mathematica

rev[n_] := FromDigits[Reverse[IntegerDigits[n]]]; a = {}; Do[d = Map[rev, Divisors[n]]; l = Length[d]; e = rev[n]; r = True; For[i = 1, i <= l, i++, If[ ! IntegerQ[e/d[[i]]], r = False]]; If[r, a = Append[a, n]], {n, 1, 200}]; a
Select[Range[200], Union[Divisible[IntegerReverse[#], IntegerReverse/@Divisors[#]]]=={True}&] (* Harvey P. Dale, Sep 04 2023 *)

Prog

(PARI) rev(n)=eval(concat(vecextract(Vec(Str(n)), "-1..1")))
is(n)=my(r=rev(n)); fordiv(n, d, if(r%rev(d), return(0))); 1 \\ Charles R Greathouse IV, Sep 12 2012

Crossrefs

Sequence in context: A175772 A124868 A165209 * A122427 A161597 A320320

Adjacent sequences: A072224 A072225 A072226 * A072228 A072229 A072230

Keyword

base,easy,nonn

Author

Joseph L. Pe, Jul 05 2002

Status

approved