A348758 Times on a 12-hour digital clock with 6 digits at which the angle of the sector enclosing the three continuously moving hands of an analog clock has a local minimum.

0, 10505, 21111, 31616, 42122, 52727, 63233, 73838, 84344, 94849, 105455, 120000

Offset: 1

Author

Hugo Pfoertner, Oct 31 2021

Keywords

• nonn
• base
• fini
• full

Comments

The inclusion of the second hand leads to solutions differing from those of A120500. Apart from the perfect match at midnight or noon, the other minima are characterized by small angles > 0 between the hour and the minute hands and a coincidence of the second hand with one of the other two hands. It turns out that the coincidence of the minute and second hands never leads to the smaller angle value. The exact times in seconds are given by A348759, with rounding to nearest second applied to determine the terms of this sequence.

Examples

			See A348759.
		

Crossrefs

Cf. A120500, A347040, A348759.

Programs

PARI

vector(12, i, my(t=((i-1)*719\/11)*43200\/719); t\3600*10000 + t%3600\60*100 + t%60) \\ Ruud H.G. van Tol, Jan 07 2025

Formula

a(n) = round(A348759(n)*43200/719) seconds since 00:00:00, expressed as hhmmss. - Robert B Fowler, Jan 05 2023