A376303 Numbers k such that no 7-smooth number ends in k.

11, 13, 17, 19, 31, 33, 37, 39, 51, 53, 55, 57, 59, 65, 71, 73, 77, 79, 85, 91, 93, 95, 97, 99, 102, 106, 110, 111, 113, 114, 117, 118, 119, 130, 131, 133, 137, 139, 142, 146, 151, 153, 154, 155, 157, 158, 159, 165, 170, 171, 173, 177, 179, 182, 185, 186, 190, 191, 193, 194, 195, 197, 198, 199

Offset

1,1

Comments

Numbers k such that A376301(k) = -1.

Numbers k such that every number ending in k is divisible by a prime >= 11.

If i*k is a term where 2 <= i <= 9 and i*k has the same number of digits as k, then k is a term.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

The multiplicative order of 3 mod 100 is 20, and that of 7 is 4.  Of the 36 numbers from 10 to 99 that are coprime to 10, the only ones congruent to some 3^i * 7^j (mod 100) are those where i = 0 to 19 and j = 0 to 3: 21, 23, 27, 29, 41, 43, 47, 49, 61, 63, 67, 69, 81, 83, 87, and 89.  The remaining 20: 11, 13, 17, 19, 31, 33, 37, 39, 51, 53, 57, 59, 71, 73, 77, 79, 91, 93, 97, 99, are members of this sequence.

Maple

dmax:= 3:  # for terms < 10^dmax
N:= 10^dmax-1: R:= NULL:
with(priqueue):
V[0]:= 10:
for d from 1 to dmax do
  A:= Array(0..10^d-1, -1);
  initialize(pq);
  insert([-1, 0, 0, 0, 0], pq);
  while pq[0] <> 0 do
    t:= extract(pq);
    x:= -t[1];
    xd:= x mod 10^d;
    if A[xd] = -1 then
      A[xd]:= x;
      insert([-7*x, t[2], t[3], t[4], t[5]+1], pq);
      if t[5] = 0 then
        insert([-5*x, t[2], t[3], t[4]+1, 0], pq);
      if t[4] = 0 then
        insert([-3*x, t[2], t[3]+1, 0, 0], pq);
      if t[3] = 0 then
        insert([-2*x, t[2]+1, 0, 0, 0], pq);
  fi fi fi fi od;
  R:= R, op(select(t -> A[t] = -1, {$10^(d-1)..10^d-1}))):
od:
R;

Crossrefs

Cf. A002473, A376301.

Sequence in context: A356466 A168446 A275467 * A045798 A267277 A155071

Adjacent sequences: A376300 A376301 A376302 * A376304 A376305 A376306

Keyword

nonn,base

Author

Robert Israel, Sep 19 2024

Status

approved