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

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

Offset: 1

Author

Shyam Sunder Gupta, Sep 22 2013

Keywords

• nonn
• base
• fini
• full
• less

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

Cf. A213182, A227407, A227410.

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