A236403 Numbers not in A236402.

11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 48, 49, 51, 52, 53, 54, 55, 56, 57, 58, 59, 61, 62, 63, 64, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 76, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 92, 93, 94, 95, 96, 97, 98, 99, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119

Offset: 1

Author

Eric Angelini, Jan 30 2014

Keywords

• nonn
• base

Comments

This sequence has density 0, since all numbers except a thin fraction have digits 0 through 18 in base 100. In particular, there are at most x^0.99782 members up to x for large enough x. (This can be improved.) - Charles R Greathouse IV, Jan 30 2014

Where does this first differ from A038687? - R. J. Mathar, Feb 03 2014

Is this a shifted version of A031954? - R. J. Mathar, Feb 03 2014

Crossrefs

Subsequence of A052382.

Cf. A236402.

Programs

PARI

is(n)=my(d=digits(n), S=Set(d), v=List()); for(i=2, #d, listput(v, 10*d[i-1]+d[i])); S=setunion(S,Set(v)); for(i=2, #d, if(!setsearch(S, d[i-1]+d[i]), return(1))); 0 \\ Charles R Greathouse IV, Mar 10 2021

Python

def ok(n):
  s = str(n)
  return not all(str(sum(map(int, s[i:i+2]))) in s for i in range(len(s)-1))
print(list(filter(ok, range(120)))) # Michael S. Branicky, Jun 11 2021

Extensions

Missing a(82) added by Charles R Greathouse IV, Mar 10 2021