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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

%I

%S 0,17,34,52,69,85,101,116,131,146,161,176,191,206,221,236,251,266,281,

%T 295,309,323,337,351,365,382,399,417,434,450,466,481,496,511,526,541,

%U 556,571,586,601,616,631,646,660,674,688,702,716,730,747,764,782,799,815,831,846,861,876,891

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

%C 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

%e 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.

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

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

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

%t total/@Range[0,100]

%Y Cf. A000040.

%K easy,nonn

%O 0,2

%A _Ivan N. Ianakiev_, Jan 30 2016

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Last modified March 22 12:46 EDT 2019. Contains 321421 sequences. (Running on oeis4.)