A247201 Numbers n whose reversal divides n+1.

1, 10, 41, 73, 100, 793, 1000, 7993, 9100, 9320, 10000, 73000, 79993, 100000, 340000, 735221, 799993, 1000000, 3070000, 7999993, 9382711, 9910000, 10000000, 73000000, 79000000, 79999993, 100000000, 361300000, 799999993, 1000000000, 1281010000

Offset

1,2

Comments

Similar to A160946.

Sequence is infinite because any number of the form 10^k, for k integer, belongs to the sequence. In fact Rev(10^k)=1 and (10^k + 1) / 1 = 10^k + 1. Also concat(7,9…9,3) = 73, 793, 7993, 79993, etc. is part of the sequence: Rev(concat(7,9…9,3)) = concat(3,9…9,7) and concat(7,9…9,4) / concat(3,9…9,7) = 2.

Links

Table of n, a(n) for n=1..31.

Example

Rev(1) = 1 and 2 / 1 = 2.
Rev(10) = 1 and 11 /1 = 11.
Rev(41) = 14 and 42 / 14 = 3.
Rev(73) = 37 and 74 / 37 = 2. Etc.

Maple

with(numtheory): T:=proc(w) local x, y, z; x:=0; y:=w;
for z from 1 to ilog10(w)+1 do x:=10*x+(y mod 10); y:=trunc(y/10); od; x; end;
P:=proc(q) local n; for n from 1 to q do if type((n+1)/T(n), integer)
then print(n); fi; od; end: P(10^9);

Prog

(PARI) rev(n)=s=""; for(i=1, #(d=digits(n)), s=concat(d[i], s)); eval(s)
for(n=1, 10^5, if(!((n+1)%rev(n)), print1(n, ", "))) \\ Derek Orr, Nov 26 2014

Crossrefs

Cf. A160946.

Sequence in context: A016082 A346346 A003355 * A022278 A246972 A266396

Adjacent sequences: A247198 A247199 A247200 * A247202 A247203 A247204

Keyword

nonn,base

Author

Paolo P. Lava, Nov 25 2014

Status

approved