A039949 -id:A039949 - cp's OEIS frontend

A132247 Twin primes congruent to {1, 11, 13, 17, 19, 29} mod 30.

11, 13, 17, 19, 29, 31, 41, 43, 59, 61, 71, 73, 101, 103, 107, 109, 137, 139, 149, 151, 179, 181, 191, 193, 197, 199, 227, 229, 239, 241, 269, 271, 281, 283, 311, 313, 347, 349, 419, 421, 431, 433, 461, 463, 521, 523, 569, 571, 599, 601, 617, 619, 641, 643

Offset: 1

Omar E. Pol, Aug 18 2007

Twin primes that are greater than 7. - Omar E. Pol, Oct 31 2013

C. K. Caldwell, The Prime Pages
C. K. Caldwell, Twin Primes
Omar E. Pol, Prime numbers in a sieve with 30 columns
Omar E. Pol, Sobre el patrón de los números primos

Cf. A001097, A039949, A132230, A132232-A132234, A132236, A132238-A132246, A132248-A132259.

a(n) = A001097(n+3). - Michel Marcus, Nov 03 2013

A282323 Lesser of twin primes congruent to 17 (mod 30).

Original entry on oeis.org

17, 107, 137, 197, 227, 347, 617, 827, 857, 1277, 1427, 1487, 1607, 1667, 1697, 1787, 1877, 1997, 2027, 2087, 2237, 2267, 2657, 2687, 3167, 3257, 3467, 3527, 3557, 3767, 3917, 4127, 4157, 4217, 4337, 4517, 4547, 4637, 4787, 4967, 5417, 5477, 5657, 5867, 6197

Offset: 1

Martin Renner, Feb 11 2017

nonn

The union of [this sequence and A282324] is A132242.
The union of [{3, 5}, A282321, this sequence and A060229] is the lesser of twin primes sequence A001359.
The union of [{3, 5, 7}, A282321 to A282326] is the twin primes sequence A001097.
A181605 without the 7. The proof works along the same lines as the proof in A282322. - R. J. Mathar, Feb 14 2017
Number of terms < 10^k: 0, 0, 1, 9, 64, 414, 2734, 19674, 146953, ... - Muniru A Asiru, Jan 09 2018

			From _Muniru A Asiru_, Jan 25 2018: (Start)
17 is a member because the pair (17, 19) is a twin prime, 17 < 19 and 17 mod 30 = 17.
137 is a member because the pair (137, 139) is a twin prime, 137 < 139 and 137 mod 30 = 17.
197 is a member because the pair (197, 199) is a twin prime, 197 < 199 and 197 mod 30 = 17.
(End)

Muniru A Asiru, Table of n, a(n) for n = 1..3000

Subset of A001097, A001359, A039949, A132242 and A132247.

Cf. A006512, A232880, A232881, A232882, A282321, A282322, A282324, A282326.

P:=Filtered([1..400000], IsPrime);;
P1:=List(Filtered(Filtered(List([1..Length(P)-1],n->[P[n],P[n+1]]),i->i[2]-i[1]=2),j->j[1] mod 30=17),k->k[1]);; # Muniru A Asiru, Jul 08 2017

[p: p in PrimesUpTo(7000) | IsPrime(p+2) and p mod 30 eq 17 ]; // Vincenzo Librandi, Feb 13 2017

a:={}:
for i from 1 to 1229 do
  if isprime(ithprime(i)+2) and ithprime(i) mod 30 = 17 then
    a:={op(a),ithprime(i)}:
  fi:
od:
a;

Select[17 + 30 Range[0, 220], PrimeQ[#] && PrimeQ[# + 2] &] (* Robert G. Wilson v, Jan 09 2018 *)
Select[Partition[Prime[Range[1000]],2,1],#[[2]]-#[[1]]==2&&Mod[#[[1]],30]==17&][[;;,1]] (* or *) Select[Range[17,7000,30],AllTrue[#+{0,2},PrimeQ]&] (* Harvey P. Dale, Mar 02 2024 *)

list(lim)=my(v=List(), p=2); forprime(q=3, lim+2, if(q-p==2 && q%30==19, listput(v, p)); p=q); Vec(v) \\ Charles R Greathouse IV, Feb 14 2017

A132242 Twin primes congruent to {17, 19} mod 30.

Original entry on oeis.org

17, 19, 107, 109, 137, 139, 197, 199, 227, 229, 347, 349, 617, 619, 827, 829, 857, 859, 1277, 1279, 1427, 1429, 1487, 1489, 1607, 1609, 1667, 1669, 1697, 1699, 1787, 1789, 1877, 1879, 1997, 1999, 2027, 2029, 2087, 2089, 2237, 2239, 2267, 2269, 2657, 2659

Offset: 1

Omar E. Pol, Aug 15 2007

Roger L. Bagula, Table of n, a(n) for n = 1..130
C. K. Caldwell, The Prime Pages.
C. K. Caldwell, Twin Primes.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A001097, A001359, A006512, A039949.

Cf. A132243, A132241.

a[0] = 7; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 2], {a[n],a[n] + 2}, {}], {n, 0, 1000}]] (* Roger L. Bagula, May 04 2008 *)

More terms from Roger L. Bagula, May 04 2008

A132243 Twin primes congruent to {1, 29} mod 30.

Original entry on oeis.org

29, 31, 59, 61, 149, 151, 179, 181, 239, 241, 269, 271, 419, 421, 569, 571, 599, 601, 659, 661, 809, 811, 1019, 1021, 1049, 1051, 1229, 1231, 1289, 1291, 1319, 1321, 1619, 1621, 1949, 1951, 2129, 2131, 2309, 2311, 2339, 2341, 2549, 2551, 2729, 2731, 2789

Offset: 1

Omar E. Pol, Aug 15 2007

Twin primes of the form 5*n +- 1. - Bruno Berselli, Aug 26 2014

Roger L. Bagula, Table of n, a(n) for n = 1..144
C. K. Caldwell, The Prime Pages.
C. K. Caldwell, Twin Primes.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A001097, A001359, A006512, A039949, A129805, A132240.

a[0] = 9; a[n_] := a[n] = a[n - 1] + 10; Flatten[Table[If[PrimeQ[a[n]] && PrimeQ[a[n] + 2], {a[n],a[n] + 2}, {}], {n, 0, 300}]] (* Roger L. Bagula, May 04 2008 *)
Flatten[Select[#+{-1,1}&/@(5*Range[0,600,2]),AllTrue[#,PrimeQ]&]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 21 2020 *)

More terms from Roger L. Bagula, May 04 2008

A132241 Twin primes congruent to {11, 13} mod 30.

Original entry on oeis.org

11, 13, 41, 43, 71, 73, 101, 103, 191, 193, 281, 283, 311, 313, 431, 433, 461, 463, 521, 523, 641, 643, 821, 823, 881, 883, 1031, 1033, 1061, 1063, 1091, 1093, 1151, 1153, 1301, 1303, 1451, 1453, 1481, 1483, 1721, 1723, 1871, 1873

Offset: 1

Omar E. Pol, Aug 15 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
C. K. Caldwell, Twin Primes.

Cf. A000040, A001097, A001359, A006512, A039949, A068231.

a[0]=1;a[n_]:=a[n]=a[n-1]+10;Flatten[Table[If[PrimeQ[a[n]]&&PrimeQ[a[n]+2],{a[n],a[n]+2},{}],{n,0,200}]] (* Vincenzo Librandi, Aug 15 2012 *)

A141860 Primes congruent to 2 mod 15.

Original entry on oeis.org

2, 17, 47, 107, 137, 167, 197, 227, 257, 317, 347, 467, 557, 587, 617, 647, 677, 797, 827, 857, 887, 947, 977, 1097, 1187, 1217, 1277, 1307, 1367, 1427, 1487, 1607, 1637, 1667, 1697, 1787, 1847, 1877, 1907, 1997, 2027, 2087, 2207, 2237, 2267, 2297, 2357, 2417

Offset: 1

N. J. A. Sloane, Jul 11 2008

2, and primes congruent to 17 mod 30. - Robert Israel, Jan 19 2016

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

[ p: p in PrimesUpTo(5000) | p mod 15 eq 2 ]; // Vincenzo Librandi, Apr 19 2011

select(isprime, [2, seq(i,i=17..1000, 30)]); # Robert Israel, Jan 19 2016

Select[Prime[Range[400]],MemberQ[{2},Mod[#,15]]&] (* Vincenzo Librandi, Aug 15 2012 *)
Select[Range[2,2500,15],PrimeQ] (* Harvey P. Dale, Dec 08 2012 *)

lista(nn) = for(n=0, nn, if(ispseudoprime(p=15*n+2), print1(p, ", "))); \\ Altug Alkan, Jan 19 2016

{2} UNION A039949. - R. J. Mathar, Jul 20 2008

A132237 Primes congruent to {7, 23} mod 30.

Original entry on oeis.org

7, 23, 37, 53, 67, 83, 97, 113, 127, 157, 173, 233, 263, 277, 293, 307, 337, 353, 367, 383, 397, 443, 457, 487, 503, 547, 563, 577, 593, 607, 653, 683, 727, 743, 757, 773, 787, 863, 877, 907, 937, 953, 967, 983, 997, 1013, 1087, 1103

Offset: 1

Omar E. Pol, Aug 15 2007

Up to 4913, there are more primes of this form than composites. See also A132231 and A227869 (congruent to 7 only). - M. F. Hasler, Nov 02 2013

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A007510, A039949, A068229, A129807.

[ p: p in PrimesUpTo(1300) | p mod 30 in [7, 23] ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[1000]],MemberQ[{7,23},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)

is_A132237(n)=setsearch([7,23],n%30)&&isprime(n) \\ - M. F. Hasler, Nov 02 2013

A132238 Primes congruent to {11, 13} mod 30.

Original entry on oeis.org

11, 13, 41, 43, 71, 73, 101, 103, 131, 163, 191, 193, 223, 251, 281, 283, 311, 313, 373, 401, 431, 433, 461, 463, 491, 521, 523, 613, 641, 643, 673, 701, 733, 761, 821, 823, 853, 881, 883, 911, 941, 971, 1031, 1033, 1061, 1063

Offset: 1

Omar E. Pol, Aug 15 2007

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A001097, A001359, A006512, A039949, A068231.

[ p: p in PrimesUpTo(1300) | p mod 30 in {11, 13} ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[200]],MemberQ[{11,13}, Mod[#,30]]&]  (* Harvey P. Dale, Mar 12 2011 *)

A253624 Initial members of prime sextuples (p, p+2, p+12, p+14, p+24, p+26).

Original entry on oeis.org

5, 17, 1277, 4217, 21587, 91127, 103967, 113147, 122027, 236867, 342047, 422087, 524957, 560477, 626597, 754967, 797567, 909317, 997097, 1322147, 1493717, 1698857, 1748027, 1762907, 2144477, 2158577, 2228507, 2398157, 2580647, 2615957

Offset: 1

Karl V. Keller, Jr., Jan 06 2015

nonn

This sequence is primes p for which there exist three twin prime pairs (p, p+2), (p+12, p+14) and (p+24, p+26).
Excluding 5, this is a subsequence of each of the following: A128468 (a(n)=30n+17). A039949 (Primes of the form 30n-13), A181605 (twin primes ending in 7).
Note that not in all cases (p, p+2, p+12, p+14, p+24, p+26) are consecutive primes; the first p's for which (p, p+2, p+12, p+14, p+24, p+26) are consecutive primes are 4217, 21587, 91127, 103967, 236867, 342047, 422087, 560477, 797567, 909317, 1322147, 1493717, 1748027, 1762907, 2144477, 2158577, 2228507, 2615957 (not in OEIS). - Zak Seidov, May 16 2017

			For p = 17, the numbers 17, 19, 29, 31, 41, 43 are primes.

Karl V. Keller, Jr., Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Twin Primes
Wikipedia, Twin prime

Cf. A077800 (twin primes), A128468, A039949, A181605.

select(t -> andmap(isprime, [t,t+2,t+12,t+14,t+24,t+26]),
[5, seq(30*k+17,k=0..10^5)]); # Robert Israel, Jan 07 2015

Select[Prime@ Range[2*10^5], Times @@ Boole@ PrimeQ[# + {2, 12, 14, 24, 26}] == 1 &] (* Michael De Vlieger, May 16 2017 *)
Select[Prime[Range[200000]],AllTrue[#+{2,12,14,24,26},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 15 2021 *)

from sympy import isprime
for n in range(1,10000001,2):
  if isprime(n) and isprime(n+2) and isprime(n+12) and isprime(n+14) and isprime(n+24) and isprime(n+26): print(n,end=', ')

from sympy import isprime, primerange
def aupto(limit):
  alst = []
  for p in primerange(2, limit+1):
    if all(map(isprime, [p+2, p+12, p+14, p+24, p+26])): alst.append(p)
  return alst
print(aupto(3*10**6)) # Michael S. Branicky, May 17 2021

A132240 Primes congruent to {1, 29} mod 30.

Original entry on oeis.org

29, 31, 59, 61, 89, 149, 151, 179, 181, 211, 239, 241, 269, 271, 331, 359, 389, 419, 421, 449, 479, 509, 541, 569, 571, 599, 601, 631, 659, 661, 691, 719, 751, 809, 811, 839, 929, 991, 1019, 1021, 1049, 1051, 1109, 1171, 1201, 1229, 1231

Offset: 1

Omar E. Pol, Aug 15 2007

For every prime p here, the cyclotomic polynomial Phi(15p,x) is flat.

Primes in A175887. [Reinhard Zumkeller, Jan 07 2012]

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A000040, A001097, A001359, A006512, A039949, A057204, A068228, A087715, A129805, A117223, A010051.

a132240 n = a132240_list !! (n-1)
a132240_list = [x | x <- a175887_list, a010051 x == 1]
-- Reinhard Zumkeller, Jan 07 2012

[ p: p in PrimesUpTo(1300) | p mod 30 in {1, 29} ]; // Vincenzo Librandi, Aug 14 2012

Select[Prime[Range[1000]],MemberQ[{1,29},Mod[#,30]]&] (* Vincenzo Librandi, Aug 14 2012 *)
Select[Flatten[#+{1,29}&/@(30Range[0,50])],PrimeQ] (* Harvey P. Dale, Sep 08 2021 *)

cp's OEIS Frontend

A132247 Twin primes congruent to {1, 11, 13, 17, 19, 29} mod 30.

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A282323 Lesser of twin primes congruent to 17 (mod 30).

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A132242 Twin primes congruent to {17, 19} mod 30.

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A132243 Twin primes congruent to {1, 29} mod 30.

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A132241 Twin primes congruent to {11, 13} mod 30.

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A141860 Primes congruent to 2 mod 15.

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A132237 Primes congruent to {7, 23} mod 30.

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A132238 Primes congruent to {11, 13} mod 30.

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