cp's OEIS Frontend

A354422 a(n) is the number of prime dates based on the proleptic Gregorian calendar in YY..YMMDD format in the year AD n, where n = YY..Y.

%I A354422 #43 Jun 05 2022 11:48:17
%S A354422 32,39,32,33,31,38,33,38,32,37,37,32,33,35,35,29,27,26,31,28,39,27,28,
%T A354422 26,24,28,31,32,33,24,28,29,32,30,25,26,23,31,32,30,33,25,25,32,33,27,
%U A354422 31,32,23,38,34,29,28,28,32,26,32,24,25,29,28,34,26,23,27
%N A354422 a(n) is the number of prime dates based on the proleptic Gregorian calendar in YY..YMMDD format in the year AD n, where n = YY..Y.
%C A354422 a(2) = a(21) = 39 seems to be the maximum. a(1220) = a(1342) = 12 is the minimum for n <= 2243. The first year with only one prime date is AD 963034 (on Nov 11), and the first year without any prime date is AD 13446204.
%e A354422 a(2022) = 23 because, in the year 2022, there are 23 prime dates: Jan 3, 19, 21 & 27; Feb 17; Mar 7, 11, 23 & 31; Apr 7; May 17; Jun 1 & 19; Jul 13; Aug 17 & 21; Sep 1 & 23; Oct 9 & 27; Nov 27; and Dec 13 & 31.
%o A354422 (Python)
%o A354422 def A354422(n):
%o A354422     from sympy import isprime; ct = 0
%o A354422     for m in range(1, 13):
%o A354422         d_max = 31 if m in {1, 3, 5, 7, 8, 10, 12} else 30 if m in {4, 6, 9, 11} else 28 if (n%4 or (n%400 and not n%100)) else 29
%o A354422         for d in range(1, d_max + 1, 2):
%o A354422             if isprime(n*10000 + m*100 + d): ct += 1
%o A354422     return ct
%Y A354422 Cf. A352947.
%K A354422 nonn,base
%O A354422 1,1
%A A354422 _Ya-Ping Lu_, Jun 04 2022