A244286 - OEIS

A244286

Consider a decimal number of k>=2 digits x = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + ... + d_(2)*10 + d_(1) and the transform T(x)-> (d_(k)+d_(k-1) mod 10)*10^(k-1) + (d_(k-1)+d_(k-2) mod 10)*10^(k-2) + ... + (d_(2)+d_(1) mod 10)*10 + (d_(1)+d(k) mod 10). Sequence lists the numbers x such that T(x) divides x.

%I #21 Oct 21 2014 00:03:24

%S 66,374,464,550,646,648,666,828,2847,5566,6468,6666,8283,19142,37398,

%T 46463,46464,46560,55550,55660,64646,66666,82029,373758,374374,464464,

%U 464640,550550,555500,646646,648648,648912,666666,737374,737484,823170,828289,828291

%N Consider a decimal number of k>=2 digits x = d_(k)*10^(k-1) + d_(k-1)*10^(k-2) + ... + d_(2)*10 + d_(1) and the transform T(x)-> (d_(k)+d_(k-1) mod 10)*10^(k-1) + (d_(k-1)+d_(k-2) mod 10)*10^(k-2) + ... + (d_(2)+d_(1) mod 10)*10 + (d_(1)+d(k) mod 10). Sequence lists the numbers x such that T(x) divides x.

%H Paolo P. Lava, <a href="/A244286/b244286.txt">Table of n, a(n) for n = 1..100</a>

%e For X = 66 -> T(x) = 22 and 66 / 22 = 3.

%e For x = 37398 -> T(x) = 00271 and 37398 / 271 = 138.

%e For x = 295248676 -> T(x) = 147624338 and 295248676 / 147624338 = 2.

%p P:=proc(q) local a,b,c,j,n; for n from 10 to q do a:=[]; b:=n;

%p while b>0 do a:=[b mod 10, op(a)]; b:=trunc(b/10); od; b:=(a[nops(a)]+a[1]) mod 10;

%p c:=0; for j from 1 to nops(a)-1 do c:=c*10+((a[j]+a[j+1]) mod 10); od; c:=c*10+b;

%p if c>0 then if type(n/c,integer) then print(n); fi; fi; od; end: P(10^9);

%o (PARI) plt(n) = {d = digits(n); nd = vector(#d, i, if (i<#d, d[i] + d[i+1], d[#d] + d[1])) % 10; subst(Pol(nd), x, 10); }

%o isok(n) = plt(n) && ((n % plt(n)) == 0); \\ _Michel Marcus_, Jul 03 2014

%Y Cf. A243993, A243994, A244287.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Jun 25 2014