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.

66, 374, 464, 550, 646, 648, 666, 828, 2847, 5566, 6468, 6666, 8283, 19142, 37398, 46463, 46464, 46560, 55550, 55660, 64646, 66666, 82029, 373758, 374374, 464464, 464640, 550550, 555500, 646646, 648648, 648912, 666666, 737374, 737484, 823170, 828289, 828291

Offset

1,1

Links

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

Example

For X = 66 -> T(x) = 22 and 66 / 22 = 3.
For x = 37398 -> T(x) = 00271 and 37398 / 271 = 138.
For x = 295248676 -> T(x) = 147624338 and 295248676 / 147624338 = 2.

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 c>0 then if type(n/c, integer) then print(n); fi; 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 % plt(n)) == 0); \\ Michel Marcus, Jul 03 2014

Crossrefs

Cf. A243993, A243994, A244287.

Sequence in context: A259292 A258958 A120102 * A223444 A084027 A063249

Adjacent sequences: A244283 A244284 A244285 * A244287 A244288 A244289

Keyword

nonn,base

Author

Paolo P. Lava, Jun 25 2014

Status

approved