A268287 - OEIS

A268287

a(n) shows how many times the sum of the hours and minutes is prime in an n-hour period starting from midnight.

0, 17, 34, 52, 69, 85, 101, 116, 131, 146, 161, 176, 191, 206, 221, 236, 251, 266, 281, 295, 309, 323, 337, 351, 365, 382, 399, 417, 434, 450, 466, 481, 496, 511, 526, 541, 556, 571, 586, 601, 616, 631, 646, 660, 674, 688, 702, 716, 730, 747, 764, 782, 799, 815, 831, 846, 861, 876, 891

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,2

COMMENTS

Partial sums of the sequence formed by repeating [17, 17, 18, 17, 16, 16, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 14, 14, 14, 14, 14, 14]. - Michel Marcus, Feb 01 2016

LINKS

Table of n, a(n) for n=0..58.

EXAMPLE

In the first one-hour period, i.e. between 0:00 and 0:59, there are PrimePi(59) - PrimePi[0] = 17 primes, therefore a(1) = 17.

MATHEMATICA

days[n_]:=Floor[n/24]; hours[n_]:=n-24*days[n];

len[n_]:=If[hours[n]==0, 0, Length[Select[Flatten[Table[Table[h+m, {m, 0, 59}], {h, 0, hours[n]-1}]], PrimeQ]]];

total[n_]:=365*days[n]+len[n];

total/@Range[0, 100]

CROSSREFS

Cf. A000040.

Sequence in context: A033014 A070814 A188290 * A249988 A098365 A033899

Adjacent sequences: A268284 A268285 A268286 * A268288 A268289 A268290

KEYWORD

easy,nonn

AUTHOR

Ivan N. Ianakiev, Jan 30 2016

STATUS

approved