cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A227409 Prime numbers representing a date in "condensed American notation" MMDDYY.

Original entry on oeis.org

10103, 10111, 10133, 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, 10433
Offset: 1

Views

Author

Shyam Sunder Gupta, Sep 22 2013

Keywords

Comments

For February, the number of days will be 28 only, as the year cannot be a leap year if MMDDYY is to be a prime number.
The sequence is finite, with 3379 terms. The largest term is a(3379)=123191.

Examples

			a(1)=10103 is prime and represents a date in MMDDYY format as 010103.
		

Crossrefs

Programs

  • Mathematica
    t = {}; Do[If[m < 8, If[OddQ[m], b = 31, If[m == 2, b = 28, b = 30]],If[OddQ[m], b = 30, b = 31]]; Do[a = 100 d + y + 10000 m;If[PrimeQ[a], AppendTo[t, a]], {d, 1, b}], {m, 1, 12}, {y, 1, 99}]; Union[t]

A227411 Palindromic prime numbers representing a date in "condensed European notation" DDMMYY.

Original entry on oeis.org

10301, 10501, 10601, 30103, 30203, 30403, 30703, 30803, 31013, 70207, 70507, 70607, 90709, 91019
Offset: 1

Views

Author

Shyam Sunder Gupta, Sep 22 2013

Keywords

Comments

For February, the number of days will be 28 only, as year cannot be a leap year for DDMMYY to be a prime number.
The sequence is finite, with 14 terms. The largest term is a(14)=91019.
There are no 6-digit solutions - the month must be 11 and the day cannot start with a 0 or a 2. Nor can the day start with a 1 because this makes the palindrome of the form 1x11x1 - divisible by 1001. This leaves only 301103, which is 11*31*883, so not prime. - Jon Perry, Sep 23 2013

Examples

			a(1)=10103 is prime and represents a date in DDMMYY format as 010103.
		

Crossrefs

Programs

  • Mathematica
    palindromicQ[n_] := TrueQ[IntegerDigits[n] == Reverse[IntegerDigits[n]]]; t = {}; Do[If[m < 8, If[OddQ[m], b = 31, If[m == 2, b = 28, b = 30]], If[OddQ[m], b = 30, b = 31]]; Do[a = 100 m + y + 10000 d; If[PrimeQ[a] && palindromicQ[a], AppendTo[t, a]], {d, 1, b}], {m, 1, 12}, {y, 1, 99}]; Union[t]

Extensions

Incorrect a(15)-a(32) from Vincenzo Librandi, Sep 23 2013 removed. - Jon Perry, Sep 24 2013

A352947 Prime numbers representing a date based on the proleptic Gregorian calendar in YY..YMMDD format.

Original entry on oeis.org

10103, 10111, 10211, 10223, 10301, 10303, 10313, 10321, 10331, 10427, 10429, 10501, 10513, 10529, 10531, 10601, 10607, 10613, 10627, 10709, 10711, 10723, 10729, 10831, 10903, 10909, 11003, 11027, 11113, 11117, 11119, 11213, 20101, 20107, 20113, 20117, 20123
Offset: 1

Views

Author

Ya-Ping Lu, Apr 10 2022

Keywords

Examples

			20050403 is a term because the date 'Apr 3, 2005' represented in YY..YMMDD format is 20050403, which is a prime number.
		

Crossrefs

Programs

  • Python
    from sympy import isprime
    for y in range(1, 3):
        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 (y%4 or (y%400 and not y%100)) else 29
            for d in range(1, d_max + 1):
                date = 10000*y + 100*m + d
                if isprime(date): print(date, end = ', ')
Showing 1-3 of 3 results.