%I #16 May 27 2024 12:22:55

%S 101,401,601,701,1201,1301,1601,1801,1901,2801,3001,103,503,1103,1303,

%T 2003,2203,2503,2803,2903,107,307,607,907,1307,1607,1907,2207,2707,

%U 109,409,509,709,809,1009,1109,1409,1609,1709,2309,2609,2909,211,311,811,911,1511,1811,2011,2111,2311,2411,2711,3011

%N The 54 prime dates of each year of the form concatenate(day,month) with leading zero for months 1, 3, 7, 9 (no leading zero for days).

%C All these dates come from January, March, July, September and November, sorted this d.m way, with 11, 9, 9, 13 and 12 dates, respectively, summing to 54. Note that all September dates without leading zero of month m = 9 from A327346 survive after inserting the 0. The November dates coincide, of course.

%t Select[Flatten@ Map[Function[{m, d}, Array[FromDigits[IntegerDigits[#]~Join~m] &, d]] @@ {PadLeft[IntegerDigits@ #, 2], Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 28, True, 31]} &, Select[Range[1, 12, 2], CoprimeQ[#, 10] &]], PrimeQ] (* _Michael De Vlieger_, Oct 03 2019 *)

%Y Cf. A062800 (first 11 members), A101780 (9 members, starting with n = 2), A166547 (9 members, starting with n = 2), A166560 (first 13 members), A167442 (12 members, starting with n = 2), respectively.

%Y Cf. A327346 (74 prime dates d.m without leading 0 for month), A327348 (66 prime dates m.d for non-leap years), A327349 (67 prime dates, like A327348 but for leap years), A327914 (58 prime dates m.d for non-leap years, with leading 0 for d = 1..9), A327915 (59 prime dates, like A327914, but for leap years).

%K nonn,easy,fini,full

%O 1,1

%A _Wolfdieter Lang_, Sep 30 2019