A244287 - OEIS

%I #16 Jul 12 2014 17:51:57

%S 11,19,22,28,33,37,44,46,55,64,73,82,91,111,157,222,333,444,555,1111,

%T 1919,2222,2828,3333,3737,4444,4646,5555,6464,7373,8282,9191,11111,

%U 22222,33333,44444,55555,111111,157157,191919,222222,282828,333333,373737,444444

%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 x divides T(x).

%H Paolo P. Lava, <a href="/A244287/b244287.txt">Table of n, a(n) for n = 1..100</a>

%e For x = 11 -> T(x) = 22 and 22 / 11 = 2.

%e For x = 19 -> T(x) = 0 and 0 /19 = 0.

%e For x = 157157 -> T(x) = 628628 and 628628 / 157157 = 4.

%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 type(c/n,integer) then print(n); 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 ) == 0); \\ _Michel Marcus_, Jul 03 2014

%Y Cf. A243993, A243994, A244286.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_, Jun 25 2014