|
%I #25 May 31 2023 15:38:24
%S 11,31,41,61,71,101,131,151,181,191,211,241,251,271,281,311,13,23,43,
%T 53,73,83,103,113,163,173,193,223,233,263,283,293,313,17,37,47,67,97,
%U 107,127,137,157,167,197,227,257,277,307,317,19,29,59,79,89,109,139,149,179,199,229,239,269,211,311,811,911,1511,1811,2011,2111,2311,2411,2711,3011
%N The 74 prime dates of each year of the form concatenate(day,month) without leading zeros for month (and day), sorted by date, including duplicates.
%C All these prime dates come from January, March, July, September and November, in the form d.m with no 0 in front of the months m = 1, 3, 7, and 9, with 16, 17, 16, 13 and 12 dates, respectively, which sum to 74.
%C There are just two duplicates, 211 (Jan. 21 and Nov. 2) and 311 (Jan. 31 and Nov. 3).
%t Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[IntegerDigits[#]~Join~m] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 28, True, 31]} &, 12], PrimeQ] (* _Michael De Vlieger_, Oct 03 2019 *)
%Y Cf. A030430 (first 16 members), A030431 (17 members, starting with n = 2), A030432 (16 members starting with n = 2), A030433 (first 13 members), A167442 (12 members starting with n = 2).
%Y Cf. A327347 (54 prime dates d.m with leading 0 for months m = 1, 3, 7, 9), 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 in 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
|
