

A268287


a(n) shows how many times the sum of the hours and minutes is prime in an nhour 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
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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 onehour 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_]:=n24*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



