A335789 a(n) = time to the nearest second at the n-th instant (n>=0) when the hour and minute hands on a clock face coincide, starting at time 0:00.

0, 3927, 7855, 11782, 15709, 19636, 23564, 27491, 31418, 35345, 39273, 43200, 47127, 51055, 54982, 58909, 62836, 66764, 70691, 74618, 78545, 82473, 86400, 90327, 94255, 98182, 102109, 106036, 109964, 113891, 117818, 121745, 125673, 129600, 133527, 137455, 141382

Offset

0,2

Comments

After 12 hours or 43200 seconds, the hands overlap at 12:00 and the cycle repeats.

Links

Table of n, a(n) for n=0..36.

Mathlete's Corner, How many times during the day do the hands of a clock overlap?

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

Formula

a(n) = round(n*43200/11).

Example

For n=1, 3927 would correspond to slightly after 01:05.

Prog

(SageMath)
L=[]
n=0
while n<50:
    L.append(round(numerical_approx((n+n/11))*3600))
    n+=1
print(L)

Crossrefs

Cf. A120500 (as HHMMSS).

Sequence in context: A229642 A266060 A034283 * A250671 A179139 A014887

Adjacent sequences: A335786 A335787 A335788 * A335790 A335791 A335792

Keyword

nonn

Author

Sean Lestrange, Aug 14 2020

Status

approved