A192130 Numbers k such that k divided by the number constructed from a decimal point followed by the reversed digits of k is an integer, but not a power of ten.

21, 42, 51, 52, 54, 57, 63, 81, 84, 210, 231, 270, 297, 420, 462, 510, 520, 521, 522, 528, 540, 561, 570, 572, 573, 594, 610, 630, 693, 810, 840, 861, 891, 2100, 2121, 2178, 2300, 2310, 2331, 2530, 2541, 2700, 2727, 2751, 2961, 2970, 2997, 4032, 4200, 4242

Offset

1,1

Comments

Quotients equal to a power of 10 are excluded to eliminate trivial cases, e.g., 777/.777 = 1000.

If k is in this sequence, so is 10*k. However, 10*k can be in this sequence even if k is not (e.g., 270 is in the sequence even though 27 is not). - Nathaniel Johnston, Jun 23 2011

Links

Nathaniel Johnston, Table of n, a(n) for n = 1..750

Example

a(1) = 21 because 21/.12 = 175;
a(6) = 57 because 57/.75 = 76.

Maple

isA192130 := proc(n) local d, m: d:=convert(n, base, 10): m:=n/add(d[j]*10^(-j), j=1..nops(d)): return `if`(type(m, integer) and not type(simplify(log[10](m)), integer), n, NULL): end: seq(isA192130(n), n=1..4410); # Nathaniel Johnston, Jun 23 2011

Mathematica

revRec[n_, b_:10] := FromDigits[Reverse[IntegerDigits[n, b]]]/b^Length[IntegerDigits[n, b]]; Select[Range[3000], IntegerQ[#/revRec[#]] && Not[IntegerQ[Log[10, #/revRec[#]]]] &] (* Alonso del Arte, Jun 23 2011 *)

Crossrefs

Sequence in context: A120772 A260749 A040420 * A258188 A037978 A089059

Adjacent sequences: A192127 A192128 A192129 * A192131 A192132 A192133

Keyword

nonn,base

Author

Gil Broussard, Jun 23 2011

Status

approved