cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

User: Tamas Nagy

Tamas Nagy's wiki page.

Tamas Nagy has authored 5 sequences.

A358381 Primes p such that q1=6*p-1 and q2=6*p+1 are also primes (twin primes) and q1 is a Sophie Germain prime (i.e., 2*q1+1 is prime).

Original entry on oeis.org

2, 5, 7, 47, 107, 907, 2137, 2347, 3407, 4547, 4597, 8377, 9067, 9277, 9767, 14537, 16427, 18307, 19507, 19997, 23447, 23917, 26927, 27437, 28837, 29297, 33037, 37307, 38327, 45127, 46457, 50957, 52957, 55897, 59077, 59407, 60317, 63667, 65497, 69767, 74377, 77527, 86587, 86837
Offset: 1

Views

Author

Tamas Nagy, Nov 12 2022

Keywords

Comments

Except for the first 2 terms, every term's last digit is a 7 in base 10.

Links

Crossrefs

Subsequence of A060212.
Cf. A005384.

Programs

  • Maple
    filter:= p -> andmap(isprime, [p, 6*p-1, 6*p+1, 12*p-1]):
select(filter, [2,5,seq(i,i=7..10^5,10)]); # Robert Israel, Dec 23 2022
  • Mathematica
    Select[Prime[Range[8500]], PrimeQ[6*# - 1] && PrimeQ[6*# + 1] && PrimeQ[12*# - 1] &] (* Amiram Eldar, Nov 13 2022 *)

A342717 Primes q such that 15*q-4, 15*q-2, 15*q+2 and 15*q+4 are all primes.

Original entry on oeis.org

7, 13, 139, 1049, 4481, 8147, 11047, 11411, 13049, 17191, 17921, 25913, 26321, 28057, 30169, 33349, 37561, 38177, 40487, 42139, 60493, 65563, 72871, 74507, 74521, 77041, 77069, 93491, 112363, 127849, 130621, 138389, 142787, 144577, 145109, 158227, 161561, 165311
Offset: 1

Views

Author

Tamas Nagy, Mar 19 2021

Keywords

Comments

The 4 generated primes always end with 1, 3, 7, 9 in base 10 in this order.

Examples

			a(1) = 7 is a term since 7 is prime and 101, 103, 107, 109 are also prime.
Some larger examples include:
  171850185252132304529579363573540628229,
  204480960976715817535460959250816270267,
  338006806817314508391110932058603239271.

Programs

  • Mathematica
    Select[Prime@ Range[10^4], AllTrue[Flatten[#1 + {-#2, #2}], PrimeQ] & @@ {15 #, {2, 4}} &] (* Michael De Vlieger, Mar 19 2021 *)
  • PARI
    isok(p) = isprime(p) && isprime(15*p-4) && isprime(15*p-2) && isprime(15*p+2) && isprime(15*p+4);

A342185 Primes q such that 10*q-1 and 10*q+3 are cousin primes.

Original entry on oeis.org

2, 11, 23, 101, 149, 227, 239, 269, 353, 479, 557, 569, 647, 683, 809, 827, 983, 1289, 1607, 1619, 1823, 1901, 1907, 2039, 2213, 2411, 2447, 2843, 2879, 2957, 2963, 3011, 3119, 3257, 3389, 3557, 3671, 3833, 3923, 4001, 4019, 4397, 4943, 5099, 5309, 5441, 5471
Offset: 1

Views

Author

Tamas Nagy, Mar 04 2021

Keywords

Comments

A pair of cousin primes are primes of the form p and p+4 (where p+2 may or may not be a prime).
Generates cousin primes such that the last digits of the primes are 9 and 3 in base 10.

Crossrefs

Cf. A046132, A342184, A342183.

Programs

  • PARI
    isok(p) = isprime(p) && isprime(10*p-1) && isprime(10*p+3); \\ Michel Marcus, Mar 05 2021

A342184 Primes q such that 10*q-3 and 10*q+1 are cousin primes.

Original entry on oeis.org

7, 13, 31, 97, 109, 157, 271, 523, 601, 691, 769, 829, 1063, 1069, 1201, 1249, 1291, 1483, 1489, 1567, 1579, 1609, 1693, 1747, 1831, 2203, 2281, 2383, 2803, 2887, 2953, 3511, 3967, 4513, 4651, 5023, 5059, 5437, 5653, 5779, 5821, 6151, 6163, 6199, 6361, 6367
Offset: 1

Views

Author

Tamas Nagy, Mar 04 2021

Keywords

Comments

A pair of cousin primes are primes of the form p and p+4 (where p+2 may or may not be a prime).
Generates cousin primes such that the last digits of the primes are 7 and 1 in base 10.

Crossrefs

Cf. A046132, A342183, A342185.

Programs

  • PARI
    isok(p) = isprime(p) && isprime(10*p-3) && isprime(10*p+1); \\ Michel Marcus, Mar 05 2021

A342183 Primes q such that 15*q-2 and 15*q+2 are cousin primes.

Original entry on oeis.org

3, 7, 11, 13, 31, 41, 43, 59, 73, 113, 139, 179, 197, 211, 223, 241, 263, 277, 349, 367, 449, 563, 587, 631, 659, 683, 739, 773, 823, 829, 977, 1033, 1049, 1217, 1471, 1487, 1553, 1571, 1583, 1607, 1609, 1669, 1697, 1753, 1901, 1907, 2089, 2111, 2281, 2531
Offset: 1

Views

Author

Tamas Nagy, Mar 04 2021

Keywords

Comments

A pair of cousin primes are primes of the form p and p+4 (where p+2 may or may not be a prime).
Generates cousin primes such that the last digit of the primes are 3 and 7 in base 10.

Crossrefs

Cf. A046132, A342184, A342185.

Programs

  • PARI
    isok(p) = isprime(p) && isprime(15*p-2) && isprime(15*p+2); \\ Michel Marcus, Mar 05 2021

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