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 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
 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 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

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Last modified May 17 08:12 EDT 2021. Contains 343966 sequences. (Running on oeis4.)