A217489 Least positive integer without a digit 1, not listed earlier and not divisible by any digit of the preceding term.

2, 3, 4, 5, 6, 7, 8, 9, 20, 23, 25, 27, 29, 33, 22, 35, 26, 37, 32, 43, 34, 38, 28, 39, 40, 30, 44, 42, 45, 46, 47, 50, 24, 49, 53, 52, 57, 36, 55, 48, 54, 58, 59, 56, 62, 63, 64, 65, 67, 68, 69, 70, 60, 73, 74, 66, 75, 72, 79, 76, 80, 77, 78, 82, 83, 85, 84, 86, 87, 89, 92, 93, 88, 90

Offset: 1

Author

M. F. Hasler and Eric Angelini, Oct 04 2012

Keywords

• nonn
• base
• easy
• look

Comments

This sequence contains all terms of A052383 that are not divisible by 2520. - Peter Kagey, Nov 04 2015

From Robert Israel, Jan 03 2016: (Start)

Here is a proof of Peter Kagey's comment:

Any number x in A052383 will eventually appear in the sequence if there are infinitely many members of the sequence containing no digit that divides x.

If k in A052383 is coprime to 210 (and thus not divisible by any digit > 1), then k is in the sequence.

The numbers 2...23 with number of 2's not divisible by 3, and 5...57 with number of 5's == 2,4 or 5 (mod 6) are coprime to 210, and thus are in the sequence.

The repunits k...k with k = 5 or 7 and an even number of digits are not divisible by 2 or 3, and thus they are in the sequence.

The repunits k...k with k = 2,3,4,6,8, or 9 and number of digits not divisible by 6 are not divisible by 5 or 7, and thus they are in the sequence. Any x in A052383 not divisible by 2520 is not divisible by one of the digits 2,3,...9, and thus is in the sequence. (End)

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000
• E. Angelini, (n+1) is not divisible by any digit of n, Oct 04 2012
• E. Angelini, (n+1) is not divisible by any digit of n [Cached copy, with permission]

Crossrefs

Cf. A002275, A038603, A052383.

Sequence A217491 is a variant of the same idea (where injectivity is strengthened to strict monotonicity).

Programs

Maple

N:= 1000: # to get all terms before the first that exceeds N
A[1]:= 2:
Av:= remove(t -> has(convert(t,base,10),1),{$3..N}):
for n from 2 do
  d:= convert(convert(A[n-1],base,10),set) minus {0};
  Ad:= remove(t -> ormap(y -> t mod y = 0, d) , Av);
  if nops(Ad) = 0 then break fi;
  A[n]:= min(Ad);
  Av:= Av minus {A[n]};
od:
seq(A[i],i=1..n-1); # Robert Israel, Jan 03 2016

Mathematica

a = {2}; Do[k = 1; While[Or[First@ DigitCount@ k > 0, MemberQ[a, k], Total[Boole@ Divisible[k, #] & /@ (IntegerDigits@ a[[n - 1]] /. 0 -> Nothing)] > 0], k++]; AppendTo[a, k], {n, 2, 74}]; a (* Michael De Vlieger, Nov 05 2015 *)