A323252 Numbers k such that the numerator and denominator of the reduced fraction Sum_{i=1..k} 1/i have no digits in common.

2, 3, 5, 6, 7, 8, 10, 15

Offset

1,1

Comments

Other terms, if they exist, are at least 3*10^5. - Erich Friedman, Nov 20 2024

Links

Table of n, a(n) for n=1..8.

Example

2 is in the sequence since Sum_{i=1..2} 1/i = 1 + 1/2 = 3/2 and the numerator and denominator have no digits in common.
3 is in the sequence since Sum_{i=1..3} 1/i = 1 + 1/2 + 1/3 = 11/6 and the numerator and denominator have no digits in common.

Mathematica

Select[Range@100, Intersection @@ IntegerDigits[ Through[ {Numerator, Denominator}[ HarmonicNumber@ #]]] == {} &] (* Giovanni Resta, Sep 13 2019 *)

Prog

(PARI) isok(n) = my(h=sum(k=1, n, 1/k)); #setintersect(Set(digits(numerator(h))), Set(digits(denominator(h)))) == 0; \\ Michel Marcus, Sep 13 2019

Crossrefs

Cf. A001008, A002805.

Sequence in context: A120486 A229993 A376592 * A219255 A025501 A028758

Adjacent sequences: A323249 A323250 A323251 * A323253 A323254 A323255

Keyword

nonn,more,base

Author

Wesley Ivan Hurt, Sep 11 2019

Status

approved