A244287 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).

11, 19, 22, 28, 33, 37, 44, 46, 55, 64, 73, 82, 91, 111, 157, 222, 333, 444, 555, 1111, 1919, 2222, 2828, 3333, 3737, 4444, 4646, 5555, 6464, 7373, 8282, 9191, 11111, 22222, 33333, 44444, 55555, 111111, 157157, 191919, 222222, 282828, 333333, 373737, 444444

Offset

1,1

Links

Paolo P. Lava, Table of n, a(n) for n = 1..100

Example

For x = 11 -> T(x) = 22 and 22 / 11 = 2.
For x = 19 -> T(x) = 0 and 0 /19 = 0.
For x = 157157 -> T(x) = 628628 and 628628 / 157157 = 4.

Maple

P:=proc(q) local a, b, c, j, n; for n from 10 to q do a:=[]; b:=n;
while b>0 do a:=[b mod 10, op(a)]; b:=trunc(b/10); od; b:=(a[nops(a)]+a[1]) mod 10;
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;
if type(c/n, integer) then print(n); fi; od; end: P(10^9);

Prog

(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); }
isok(n) = ((plt(n) % n ) == 0); \\ Michel Marcus, Jul 03 2014

Crossrefs

Cf. A243993, A243994, A244286.

Sequence in context: A004750 A366195 A328870 * A065126 A284783 A145059

Adjacent sequences: A244284 A244285 A244286 * A244288 A244289 A244290

Keyword

nonn,base

Author

Paolo P. Lava, Jun 25 2014

Status

approved