A167442 -id:A167442 - cp's OEIS frontend

A244763 Prime numbers ending in the prime number 13.

13, 113, 313, 613, 1013, 1213, 1613, 1913, 2113, 2213, 2713, 3313, 3413, 3613, 4013, 4513, 4813, 5113, 5413, 5813, 6113, 7013, 7213, 8513, 8713, 9013, 9413, 9613, 10313, 10513, 10613, 11113, 11213, 11813, 12113, 12413, 12613, 12713, 13313, 13513, 13613, 13913

Offset: 1

Vincenzo Librandi, Jul 06 2014

Also primes of the form 100*n+13. Subsequence of A141885, A141937, A166573.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Cf. A141885, A141937, A166573.

Cf. Prime numbers ending in the prime number k: A030431 (k=3), A030432 (k=7), A167442 (k=11), this sequence (k=13), A244764 (k=17), A244765 (k=19), A244766 (k=23), A244767 (k=29), A167388 (k=31), A244768 (k=37), A167443 (k=41), A244769 (k=43), A244770 (k=47), A244771 (k=53), A244772 (k=59), A167445 (k=61), A244773 (k=67), A167441 (k=71), A244774 (k=73), A244775 (k=79), A244776 (k=83), A244777 (k=89), A244778 (k=97), A167626 (k=101), A167627 (k=163).

[n: n in PrimesUpTo(14000) | n mod 100 eq 13];

select(isprime, [13+100*n $ n=0..1000]); # Robert Israel, Jul 06 2014

Select[Prime[Range[5, 2000]], Take[IntegerDigits[#], -2]=={1, 3}&]

select(x->(x % 100)==13, primes(2000)) \\ Michel Marcus, Jul 06 2014

[p for p in primes(14000) if mod(p,100) == 13] # Bruno Berselli, Jul 07 2014

A327346 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.

Original entry on oeis.org

11, 31, 41, 61, 71, 101, 131, 151, 181, 191, 211, 241, 251, 271, 281, 311, 13, 23, 43, 53, 73, 83, 103, 113, 163, 173, 193, 223, 233, 263, 283, 293, 313, 17, 37, 47, 67, 97, 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

Offset: 1

Wolfdieter Lang, Sep 30 2019

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.

There are just two duplicates, 211 (Jan. 21 and Nov. 2) and 311 (Jan. 31 and Nov. 3).

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).

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).

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 *)

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).

Original entry on oeis.org

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 *)

A101471 Numbers k such that the number k11 is prime.

Original entry on oeis.org

0, 2, 3, 8, 9, 15, 18, 20, 21, 23, 24, 27, 30, 35, 39, 41, 42, 50, 57, 60, 62, 63, 69, 72, 74, 80, 81, 83, 90, 93, 95, 98, 101, 102, 107, 113, 114, 120, 122, 125, 126, 129, 134, 137, 140, 144, 155, 161, 164, 168, 170, 179, 182, 183, 189, 192, 200, 204, 206, 210, 212

Offset: 1

Parthasarathy Nambi, Jan 30 2005, Feb 18 2005

k such that 100*k+11 is prime. - Robert Israel, Jul 30 2015

			If k=2,  then k11 =  211 (prime);
If k=50, then k11 = 5011 (prime);
If k=98, then k11 = 9811 (prime).

Robert Israel, Table of n, a(n) for n = 1..10000
Chris Caldwell, The first 1,000 primes.

Cf. A024912 (10n+1 is prime), A167442 (the actual primes 100n+11).

[n: n in [0..250] | IsPrime(Seqint(Intseq(11) cat Intseq(n)))]; // Vincenzo Librandi, Jul 31 2015

[n: n in [0..240] |IsPrime(100*n+11)]; // Vincenzo Librandi, Jul 31 2015

select(t -> isprime(100*t+11), [$0..1000]); # Robert Israel, Jul 30 2015

Select[ Range[0, 215], PrimeQ[ FromDigits[ Flatten[ IntegerDigits /@ { #, 1, 1}]]] &] (* Robert G. Wilson v, Feb 21 2005 *)
Select[Range[0,250],PrimeQ[100#+11]&] (* Harvey P. Dale, Oct 11 2018 *)

is(n)=isprime(100*n+11) \\ Charles R Greathouse IV, Feb 20 2017

Corrected and extended by Robert G. Wilson v, Feb 21 2005

A238331 The prime(n)-th prime number ending in prime(n), or 0 if none exists.

Original entry on oeis.org

0, 23, 0, 107, 2411, 3413, 5417, 4919, 5923, 8629, 9931, 10937, 14741, 14243, 16747, 18553, 19259, 22961, 24767, 28571, 24373, 31079, 29483, 33589, 35597, 498101, 475103, 528107, 555109, 570113, 607127, 641131, 659137, 717139, 756149, 786151, 754157, 817163

Offset: 1

T. D. Noe, Feb 27 2014

The first number ending in prime(n) is, of course, prime(n). The numbers 2 and 5 are zero because there are no additional primes ending in those numbers; they are the numbers divisible by 2 or 5.

			23 is the third prime ending with 3.
107 is the seventh prime ending in 7.
2411 is the 11th prime ending in 11.
3413 is the 13th prime ending in 13 -- a very unlucky prime.

T. D. Noe, Table of n, a(n) for n = 1..200

Cf. A000040 (prime numbers).

Cf. A030431, A030432, A167442 (primes ending in 3, 7, 11).

ps = Prime[Range[PrimePi[1000000]]]; t = {}; p = 1; done = False; While[! done,p = NextPrime[p]; len = Length[IntegerDigits[p]]; s = Select[ps, Mod[#, 10^len] == p &, p]; If[Length[s] < p, If[MemberQ[{2, 5}, p], AppendTo[t, 0], done = True], AppendTo[t, s[[-1]]]]]; t

A110406 List of k primes ending in k, where k == 1, 3, 7 or 9 (mod 10).

Original entry on oeis.org

11, 3, 13, 23, 7, 17, 37, 47, 67, 97, 107, 19, 29, 59, 79, 89, 109, 139, 149, 179, 11, 211, 311, 811, 911, 1511, 1811, 2011, 2111, 2311, 2411, 13, 113, 313, 613, 1013, 1213, 1613, 1913, 2113, 2213, 2713, 3313, 3413, 17, 317, 617, 1117, 1217, 2017, 2417, 2617

Offset: 1

Amarnath Murthy, Jul 30 2005

Lists the 1st entry in A030430, the first 3 entries of A030431, the first 7 entries of A030432, the first 9 entries of A030433, the first 11 entries of A167442 etc.

			Terms corresponding to 7 are 7, 17, 37, 47, 67, 97, 127. 13 occurs for 3 as well as for 13.
11;
3,13,23;
7,17,37,47,67,97,107;
19,29,59,79,89,109,139,149,179;

Cf. A089779, A088262.

f[n_] := Take[ Select[p, Mod[ #, 10^Floor[ Log[10, n] + 1]] == n &], n]; p = Prime[ Range[10^5]]; lst = Select[ Range[1, 17, 2], Mod[ #, 10] != 5 &] (* Robert G. Wilson v *)

Corrected and extended by Robert G. Wilson v, Jul 30 2005

cp's OEIS Frontend

A244763 Prime numbers ending in the prime number 13.

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A327346 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.

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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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A101471 Numbers k such that the number k11 is prime.

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A238331 The prime(n)-th prime number ending in prime(n), or 0 if none exists.

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A110406 List of k primes ending in k, where k == 1, 3, 7 or 9 (mod 10).

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