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.

A327915 The 59 prime dates of each leap year of the form concatenate(month,day) with leading zero for days 1..9.

This page as a plain text file.
%I A327915 #15 Sep 01 2023 11:33:48
%S A327915 101,103,107,109,113,127,131,211,223,227,229,307,311,313,317,331,401,
%T A327915 409,419,421,503,509,521,523,601,607,613,617,619,701,709,719,727,809,
%U A327915 811,821,823,827,829,901,911,919,929,1009,1013,1019,1021,1031,1103,1109,1117,1123,1129,1201,1213,1217,1223,1229,1231
%N A327915 The 59 prime dates of each leap year of the form concatenate(month,day) with leading zero for days 1..9.
%C A327915 In leap years all these dates come from the months January, February, ..., December, in the form  m.d, with a 0 in front of the days d = 1..9, with 7, 4, 5, 4, 4, 5, 4, 6, 4, 5, 5, 6 prime dates, respectively, adding up to 59. For the corresponding leap year case with 58 prime dates see A327914.
%C A327915 Compared with A327349 (leap years, no 0's before days d = 1..9) one has the same differences as given in a comment in A327914 (229 appears in the present sequence and in A327349).
%t A327915 Select[Flatten@ Array[Function[{m, d}, Array[FromDigits[m~Join~PadLeft[IntegerDigits[#], 2]] &, d]] @@ {IntegerDigits@ #, Which[MemberQ[{4, 6, 9, 11}, #], 30, # == 2, 29, True, 31]} &, 12], PrimeQ] (* _Michael De Vlieger_, Oct 03 2019 *)
%t A327915 fd[{m_,d_}]:=FromDigits[Flatten[{m,PadLeft[{d},2,0]}]]; Select[fd[Take[#,{2,3}]]&/@ DateRange[ {2024,1,1},{2024,12,31}],PrimeQ] (* _Harvey P. Dale_, Sep 01 2023 *)
%Y A327915 Cf. A327346 (74 prime dates d.m without leading 0 for month), 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, the case for non-leap years).
%K A327915 nonn,easy,fini,full
%O A327915 1,1
%A A327915 _Wolfdieter Lang_, Sep 30 2019