A337904 Numbers k such that the decimal expansion of the k-th harmonic number starts with the digits of k, in the same order.

1, 43, 714, 715, 9763, 122968, 122969, 1478366, 17239955, 196746419, 2209316467, 24499118645, 268950072605

Offset

1,2

Comments

The sequence also includes 196746419, 2209316467, 24499118645, 268950072605, 2928264676792, 31663398162514, 340383084842938, 3640820101879826. - Daniel Suteu, Oct 01 2020

Links

Table of n, a(n) for n=1..13.

Example

1/1 + 1/2 + 1/3 + ... + 1/1478366 = 14.78366... .

Mathematica

s=0; Do[s=s+(1/n); t=IntegerLength[n]; m=IntegerLength[Floor[s]]; k = Floor[s (10^(t-m))]; If[k==n, Print[n]], {n, 1, 10^11}]

Prog

(PARI) lista(nn) = {my(s=0.); for (n=1, nn, s += 1./n; my(d = digits(floor(10^20*s))); if (fromdigits(vector(#Str(n), j, d[j])) == n, print1(n, ", ")); ); } \\ Michel Marcus, Sep 30 2020

Crossrefs

Cf. A033147, A055980.

Sequence in context: A332946 A229689 A146979 * A278174 A332910 A157722

Adjacent sequences: A337901 A337902 A337903 * A337905 A337906 A337907

Keyword

nonn,base,more

Author

Metin Sariyar, Sep 29 2020

Extensions

a(9) from Jinyuan Wang, Sep 30 2020

a(10)-a(12) from Chai Wah Wu, Oct 12 2020

a(13) from Chai Wah Wu, Oct 14 2020

Status

approved