A297778 Number of distinct runs in base-10 digits of n.

1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2

Offset: 1

Author

Clark Kimberling, Feb 03 2018

Keywords

• nonn
• base
• easy

Comments

Every positive integers occurs infinitely many times. See A297770 for a guide to related sequences. A043562(n) = a(n) for n=1..100, but not for n=101.

Examples

			14! in base-10: 2,7,0,0,1,7,3,0,1,3,0,0; ten runs, of which 6 are distinct, so that a(14!) = 6.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A043562 (number of runs, not necessarily distinct), A297770.

Programs

Mathematica

b = 10; s[n_] := Length[Union[Split[IntegerDigits[n, b]]]]
Table[s[n], {n, 1, 200}]