A048053
Smallest sequence of 12 consecutive reversible primes (emirps).
Original entry on oeis.org
9387802769, 9387802807, 9387802817, 9387802861, 9387802867, 9387802873, 9387802909, 9387802937, 9387802939, 9387802973, 9387802987, 9387803003
Offset: 1
The reverse of prime 9387802769 is 9672087839 is also prime, as are all of these numbers.
A122568
Least k (or 0 if no such k exists) such that 10^n+k is the least bemirp of a quartet of 4 different bemirps and the least bemirp of n+1 digits.
Original entry on oeis.org
0, 0, 61, 61, 6861, 106881, 806881, 688611, 6088861, 169111, 6601911, 810681, 1161, 10086091, 6096691, 1016101, 69088101, 16106811, 60088191, 8608611, 6008001, 66169881, 160161601, 106898181, 689060101, 1811106801
Offset: 1
For n=3 10^3+61=1061, 1061, 1091, 1901, 1601 are 4 bemirps so a(3)=61 as 1061 is the least 4 digits prime like this
For n=4 10^4+61=10061, 10061, 10091, 19001, 16001 are 4 bemirps so a(4)=61 as 10061 is the least 5 digits prime like this
A145750
Primes which become emirps when rotated by 180 degrees on a digital clock display.
Original entry on oeis.org
661, 1061, 1091, 1181, 1601, 1811, 1901, 6011, 6991, 10061, 10091, 10861, 11681, 16001, 16981, 19001, 19961, 60601, 60611, 69001, 106861, 108161, 108881, 109891, 110881, 116881, 116911, 118081, 118861, 119101, 119611, 160861, 161611, 168601, 169691
Offset: 1
1109 is a prime. After 2D rotation it is 6011, which is prime. However, 6011 is not an emirp because 1106 is not prime. So 1109 is not in the sequence.
1109 removed, 6011 inserted etc. by
R. J. Mathar, Apr 05 2009
A122717
Least prime P such that P is the least of bemirps of n digits and the bemirps are first of twin primes or 0 if no such primes exist.
Original entry on oeis.org
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 111696081881, 1061169181691, 0, 118181010160181
Offset: 1
111696081881 and 111696081883 twin primes,
111969081881 and 111969081883 twin primes,
188180696111 and 188180696113 twin primes,
188180969111 and 188180969113 twin primes,
so the least bemirp 111696081881 = a(12).
- Chris Caldwell, Bemirp [From _G. L. Honaker, Jr._, Oct 01 2009]
A159064
Emirps which remain primes when rotated by 180 degrees on a digital clock display.
Original entry on oeis.org
199, 1061, 1091, 1109, 1181, 1601, 1669, 1811, 1901, 10061, 10069, 10091, 10909, 11909, 16001, 18691, 18911, 19001, 19661, 19801, 101119, 101611, 106681, 106699, 106861, 108881, 109609, 109891, 110119, 110881, 110989, 111119, 111869, 111919, 116911
Offset: 1
1109 is an emirp (prime, and the reverse 9011 is also prime), it contains only digits 0,1,6,8 or 9 and can be rotated to form 6011, which is also prime. So 1109 is in the sequence.
18691 and 18911 inserted, extended by
R. J. Mathar, Apr 05 2009
A333648
Bemirp gaps: differences between consecutive bemirps.
Original entry on oeis.org
30, 510, 300, 8160, 30, 5910, 3000, 87860, 3030, 58710, 30300, 907980, 3000, 496200, 199980, 3030, 76920, 3000, 20070, 8897800, 3000, 251930, 30000, 517870, 89010, 117320, 3000, 87970, 61980, 4092720, 36980, 68020, 522380, 191620, 106230, 1621950, 7200, 620
Offset: 1
A335731
Bemirps that also interpret 2 and 5 as upside-down forms of each other, assuming a digital font.
Original entry on oeis.org
1061, 1091, 1601, 1901, 10061, 10091, 16001, 19001, 106861, 109891, 110651, 110921, 120121, 121021, 121921, 129011, 129121, 150151, 151051, 151651, 156011, 156151, 168601, 198901, 1022591, 1026521, 1028011, 1055261, 1058011, 1059251, 1069291, 1096561, 1102891, 1105861, 1106881, 1108201, 1108501, 1109881, 1111651
Offset: 1
110651 is in the list as its upside-down form 110921, and its emirp 156011, and the emirp of its upside-down form 129011, are all primes and uniquely different numbers.
Normal bemirps are defined in
A048895.
-
from sympy.ntheory import isprime as isp
def ip(pp):
rr = []
for qq in pp:
if qq=="0" or qq=="1" or qq=="8":
rr.append(qq)
elif qq=="2":
rr.append("5")
elif qq=="5":
rr.append("2")
elif qq=="6":
rr.append("9")
elif qq=="9":
rr.append("6")
return "".join(rr)
for bb in range(1,10000000):
if isp(bb):
bb = str(bb)
if ("7" not in bb) and ("4" not in bb) and ("3" not in bb):
cc = bb[::-1]
dd = ip(bb)
ee = ip(cc)
if bb!=cc and dd!=ee and bb!=dd and bb!=ee and cc!=dd and cc!=ee and isp(int(cc)) and isp(int(dd)) and isp(int(ee)):
print(bb)
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