A074822 -id:A074822 - cp's OEIS frontend

A289353 Primes p such that (p,p+4) is a pair of cousin primes and p == 7 (mod 10).

7, 37, 67, 97, 127, 277, 307, 397, 457, 487, 757, 877, 907, 937, 967, 1087, 1297, 1447, 1567, 1597, 1867, 2137, 2347, 2377, 2437, 2617, 2707, 2797, 2857, 3037, 3187, 3217, 3457, 3697, 3847, 3877, 3907, 4447, 5077, 5167, 5227, 5347, 5437, 5527, 5647, 5737, 5857, 6007, 6217, 6547, 6577

Offset: 1

Muniru A Asiru, Jul 03 2017

nonn

For cousin primes (p,p+4) such that p == 9 (mod 10), see A074822.

Members of A023200 with a last digit of 7. - Iain Fox, Dec 22 2017

			The pair of cousin prime (3,7) is not a member since 3 mod 10 = 3.
For p = 97, we get that (97,101) is a cousin prime pair and 97 == 7 (mod 10).

Muniru A Asiru, Table of n, a(n) for n = 1..10000

Cf. A001223, A001359, A023200, A046132, A074822, A160440.

P:=Filtered([1..10000],IsPrime);;
P1:=List(Filtered(Filtered(List([1..Length(P)-1],n->[P[n],P[n+1]]),i->i[2]-i[1]=4),j->j[1] mod 5 =2),k->k[1]);

a:={}: for i from 1 to 1500 do if isprime(ithprime(i)+4) and ithprime(i) mod 10 = 7 then a:={op(a),ithprime(i)}: fi: od: a; # Muniru A Asiru, Aug 04 2017

Select[10 Range[0, 660] + 7, PrimeQ[#] && PrimeQ[# + 4] &] (* Robert G. Wilson v, Dec 11 2017 *)

isok(p) = isprime(p) && isprime(p+4) && ((p % 10) == 7); \\ Michel Marcus, Jul 03 2017

is(n)=n%30==7 && isprime(n+4) && isprime(n) \\ Charles R Greathouse IV, Jul 13 2017

A119593 Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 4.

Original entry on oeis.org

67, 193, 277, 487, 613, 823, 907, 1663, 1873, 2083, 2293, 2377, 2797, 3217, 3343, 3847, 4813, 5233, 5527, 5653, 5737, 6577, 6997, 7207, 7753, 8677, 8803, 9433, 11113, 11617

Offset: 1

Rémi Eismann, Jun 01 2006, May 04 2007

The prime numbers in this sequence are of the form (14i-3) with i=(level(n)+1)/2, level(n) defined in A117563.

Remi Eismann, Table of n, a(n) for n=1..10000

Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

forprimestep(p=67,1e4,14, t=p%5; if((t==2 || t==3) && isprime(p+4), print1(p", "))) \\ Charles R Greathouse IV, Sep 17 2022

p=67; forprime(q=p+2,1e4, if(q-p==4 && (p%70==53 || p%70==67), print1(p", ")); p=q) \\ Charles R Greathouse IV, Sep 17 2022

Primes p such that (1) p = 53 or 67 mod 70 and (2) p+4 is prime. - Charles R Greathouse IV, Sep 17 2022

a(n) = Omega(n log^2 n). - Charles R Greathouse IV, Sep 17 2022

A119594 Primes for which the weight as defined in A117078 is 9 and the gap as defined in A001223 is 4.

Original entry on oeis.org

13, 103, 463, 643, 877, 967, 1093, 1597, 1867, 1993, 2137, 2857, 3037, 3163, 3253, 3613, 3793, 4153, 4513, 4783, 5413, 5503, 5647, 6007, 6043, 6547, 6907, 7537, 7573, 7933, 8167, 8293, 9157, 9337, 9463, 9787

Offset: 1

Rémi Eismann, Jun 01 2006, May 04 2007

nonn

The prime numbers in this sequence are of the form (18i-5) with i=(level(n)+1)/2, level(n) defined in A117563.

			a(1)=13 because of 17=13+mod(13;9) and 17-13=4.
18*1-5=13, level=1
a(2)=103 because of 107=103+mod(103;9) and 107-103=4
18*((11+1)/2)-5=103, level=11

Remi Eismann, Table of n, a(n) for n=1..10000

Cf. A117078, A001223, A117563, A001359, A118359, A074822, A118922, A118924, A119504.

A132255 Isolated primes congruent to {17, 19} mod 30.

Original entry on oeis.org

47, 79, 167, 257, 317, 379, 409, 439, 467, 499, 557, 587, 647, 677, 709, 739, 769, 797, 887, 919, 947, 977, 1009, 1039, 1069, 1097, 1129, 1187, 1217, 1249, 1307, 1367, 1399, 1459, 1549, 1579, 1637, 1759, 1847, 1907, 2179, 2207, 2297

Offset: 1

Omar E. Pol, Aug 20 2007

Harvey P. Dale, 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. A007510, A074822, A078857.

Select[Prime[Range[500]],NoneTrue[#+{2,-2},PrimeQ]&&MemberQ[{17,19},Mod[#,30]]&]

A289413 Primes p such that (p,p+4) is a pair of cousin primes and p == 3 (mod 10).

Original entry on oeis.org

3, 13, 43, 103, 163, 193, 223, 313, 463, 613, 643, 673, 823, 853, 883, 1093, 1213, 1303, 1423, 1483, 1663, 1693, 1783, 1873, 1993, 2083, 2203, 2293, 2473, 2683, 2833, 2953, 3163, 3253, 3343, 3463, 3613, 3673, 3793, 3943, 4003, 4153, 4513, 4783, 4813, 4933, 5233, 5413, 5503, 5653, 5923

Offset: 1

Muniru A Asiru, Jul 06 2017

nonn

For pairs of cousin primes (p,p+4) such that p == 9 (mod 10) and pairs of cousin primes (p,p+4) such that p == 7 (mod 10), see A074822 and A289353, respectively. A074822, A289353 and this sequence give all the lesser members p of pairs of cousin primes.

			For p = 193, the pair of cousin primes is (193, 197) and 193 == 3 (mod 10).
Although, the primes 3 and 7 are not consecutive primes, p = 3 yields the pair of cousin primes (3, 7) and 3 == 3 (mod 10).

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Cf. A023200, A074822, A001223, A001359, A046132, A160440, A289353.

P:=Filtered([1..10000],IsPrime);;
P1:=Concatenation([3],List(Filtered(Filtered(List([1..Length(P)-1],n->[P[n],P[n+1]]),i->i[2]-i[1]=4),j->j[1] mod 10 = 3),k->k[1]));

A289413:={}:  for i from 1 to 1500 do if isprime(ithprime(i) + 4) and ithprime(i) mod 10 = 3 then A289413:={op(A289413), ithprime(i)}: fi: od: A289413;
# Alternative:
select(t -> isprime(t) and isprime(t+4), [seq(i,i=3..10000, 10)]); # Robert Israel, Aug 02 2017

Select[Prime[Range[800]],Mod[#,10]==3&&PrimeQ[#+4]&] (* Harvey P. Dale, Aug 22 2019 *)

isok(p) = isprime(p) && isprime(p+4) && (p%10==3); \\ Michel Marcus, Jul 19 2017

list(lim)=my(v=List([3]),p=13); forprime(q=17,lim+4, if(q-p==4 && p%10==3, listput(v,p)); p=q); Vec(v) \\ Charles R Greathouse IV, Aug 03 2017

A132252 Isolated primes congruent to 19 (mod 30).

Original entry on oeis.org

79, 379, 409, 439, 499, 709, 739, 769, 919, 1009, 1039, 1069, 1129, 1249, 1399, 1459, 1549, 1579, 1759, 2179, 2389, 2539, 2719, 2749, 3019, 3049, 3079, 3109, 3229, 3319, 3499, 3709, 3739, 3889, 4099, 4729, 4759, 4909, 4999, 5059, 5119

Offset: 1

Omar E. Pol, Aug 20 2007

C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A007510, A074822.

A132257 Isolated primes congruent to {11, 13, 17, 19} mod 30.

Original entry on oeis.org

47, 79, 131, 163, 167, 223, 251, 257, 317, 373, 379, 401, 409, 439, 467, 491, 499, 557, 587, 613, 647, 673, 677, 701, 709, 733, 739, 761, 769, 797, 853, 887, 911, 919, 941, 947, 971, 977, 1009, 1039, 1069, 1097, 1123, 1129, 1181, 1187

Offset: 1

Omar E. Pol, Aug 20 2007

C. K. Caldwell, The Prime Pages.
Omar E. Pol, Determinacion geometrica de los numeros primos y perfectos.

Cf. A007510, A074822, A078857.

cp's OEIS Frontend

A289353 Primes p such that (p,p+4) is a pair of cousin primes and p == 7 (mod 10).

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A119593 Primes for which the weight as defined in A117078 is 7 and the gap as defined in A001223 is 4.

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A119594 Primes for which the weight as defined in A117078 is 9 and the gap as defined in A001223 is 4.

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A132255 Isolated primes congruent to {17, 19} mod 30.

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A289413 Primes p such that (p,p+4) is a pair of cousin primes and p == 3 (mod 10).

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Examples

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Programs

GAP

Maple

Mathematica

PARI

PARI

A132252 Isolated primes congruent to 19 (mod 30).

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A132257 Isolated primes congruent to {11, 13, 17, 19} mod 30.

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