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.

32, 39, 32, 33, 31, 38, 33, 38, 32, 37, 37, 32, 33, 35, 35, 29, 27, 26, 31, 28, 39, 27, 28, 26, 24, 28, 31, 32, 33, 24, 28, 29, 32, 30, 25, 26, 23, 31, 32, 30, 33, 25, 25, 32, 33, 27, 31, 32, 23, 38, 34, 29, 28, 28, 32, 26, 32, 24, 25, 29, 28, 34, 26, 23, 27

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..65.

Example

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.

Prog

(Python)
def A354422(n):
    from sympy import isprime; ct = 0
    for m in range(1, 13):
        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
        for d in range(1, d_max + 1, 2):
            if isprime(n*10000 + m*100 + d): ct += 1
    return ct

Crossrefs

Cf. A352947.

Sequence in context: A345491 A178099 A039778 * A217060 A326112 A363530

Adjacent sequences: A354419 A354420 A354421 * A354423 A354424 A354425

Keyword

nonn,base

Author

Ya-Ping Lu, Jun 04 2022

Status

approved