A166560 -id:A166560 - cp's OEIS frontend

A327347 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).

101, 401, 601, 701, 1201, 1301, 1601, 1801, 1901, 2801, 3001, 103, 503, 1103, 1303, 2003, 2203, 2503, 2803, 2903, 107, 307, 607, 907, 1307, 1607, 1907, 2207, 2707, 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

Offset: 1

Wolfdieter Lang, Sep 30 2019

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.

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.

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).

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 *)

A104045 Numbers k such that k9 is prime and k is a multiple of ten.

Original entry on oeis.org

10, 40, 50, 70, 80, 100, 110, 140, 160, 170, 230, 260, 290, 310, 320, 370, 440, 490, 500, 520, 530, 670, 710, 730, 800, 820, 860, 910, 920, 1000, 1070, 1090, 1190, 1210, 1240, 1280, 1300, 1310, 1330, 1370, 1400, 1580, 1720, 1750, 1760, 1790, 1900, 1930, 1960, 1970, 2050, 2080, 2210

Offset: 1

Parthasarathy Nambi, Mar 01 2005

			If k =  10, then k9 =  109 (prime).
If k = 160, then k9 = 1609 (prime).
If k = 320, then k9 = 3209 (prime).

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Cf. A030433, A008592, A102700, A166560 (resulting primes).

select(n-> isprime(10*n+9), [10*i$i=1..300])[];  # Alois P. Heinz, Jan 19 2024

Select[Range[10,2210,10],PrimeQ[FromDigits[Prepend[{9},#]]]&] (* James C. McMahon, Jan 19 2024 *)

from sympy import isprime
from itertools import count, islice
def agen(): yield from (k for k in count(10, 10) if isprime(10*k+9))
print(list(islice(agen(), 53))) # Michael S. Branicky, Jan 19 2024

cp's OEIS Frontend

A327347 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).

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A104045 Numbers k such that k9 is prime and k is a multiple of ten.

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