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.

Showing 1-10 of 11 results. Next

A145490 Numbers k such that 6k+19 is prime and absolute value of 12k+1 is also prime.

Original entry on oeis.org

-2, -1, 3, 8, 9, 13, 15, 20, 23, 29, 34, 35, 48, 55, 59, 63, 69, 73, 78, 84, 93, 100, 104, 115, 119, 134, 135, 139, 148, 150, 169, 174, 178, 185, 189, 199, 203, 210, 213, 218, 238, 254, 255, 260, 265, 268, 275, 280, 288, 289, 293, 294, 295, 308, 309, 335, 344
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

Cf. A063908-A063913, A092109, A145471-A145490.

Programs

  • Maple
    with(numtheory): a:=proc(n) if(isprime(6*n+19) and isprime(abs(12*n+1)))then return n: fi: return NULL: end: seq(a(n),n=-2..350); # Nathaniel Johnston, Jul 26 2011

Formula

a(n) = (A145480(n-2)-1)/12 for n >= 3.

Extensions

Corrected by Arkadiusz Wesolowski, Jul 26 2011

A145475 Primes p such that (17+p)/2 is prime.

Original entry on oeis.org

5, 17, 29, 41, 89, 101, 149, 197, 257, 281, 317, 449, 461, 509, 521, 569, 617, 677, 701, 761, 821, 881, 941, 1097, 1109, 1181, 1217, 1277, 1289, 1301, 1601, 1637, 1697, 1709, 1877, 1889, 1949, 2081, 2309, 2357, 2417, 2441, 2549, 2621, 2729, 2801, 2837, 2861
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 5 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 17; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(17+#)/2]&] (* Harvey P. Dale, Jan 02 2013 *)

A145472 Primes p such that (p+7)/2 is prime.

Original entry on oeis.org

3, 7, 19, 31, 67, 79, 127, 139, 151, 199, 211, 271, 307, 379, 439, 547, 607, 619, 691, 727, 739, 751, 787, 811, 859, 907, 919, 967, 991, 1039, 1087, 1231, 1279, 1447, 1459, 1471, 1531, 1567, 1699, 1747, 1759, 1831, 1867, 1987, 2011, 2131, 2179, 2239, 2251
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first one) to 7 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480, A063910.

Programs

  • Magma
    [p: p in PrimesUpTo(2500)| IsPrime((p + 7) div 2)]; // Vincenzo Librandi, Feb 04 2013
  • Mathematica
    aa = {}; k = 7; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(#+7)/2]&] (* Harvey P. Dale, Jan 11 2020 *)
  • PARI
    list(n)=my(t=1, p, i=1); while(i2&&isprime((7+p)/2), print1(n, ", "))) \\Anders Hellström, Jan 23 2017
  • PARI
    list(lim)=my(v=List()); forprime(p=3,lim, if(isprime((p+7)/2), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

A145474 Primes p such that (13+p)/2 is prime.

Original entry on oeis.org

13, 61, 73, 109, 181, 193, 241, 313, 349, 373, 409, 433, 541, 601, 613, 661, 733, 829, 853, 1033, 1069, 1129, 1201, 1213, 1249, 1453, 1489, 1609, 1693, 1741, 1753, 1801, 1861, 2029, 2053, 2089, 2113, 2161, 2221, 2293, 2389, 2593, 2749, 2833, 2953, 3049
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 1 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Maple
    select(t -> isprime(t) and isprime((13+t)/2), [seq(12*k+1, k=1..100)]); # Robert Israel, Aug 05 2014
  • Mathematica
    aa = {}; k = 13; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
  • PARI
    forprime(p=3,10^4,if(isprime((13+p)/2),print1(p,", "))) \\ Derek Orr, Aug 05 2014

A145476 Primes p such that (19 + p)/2 is prime.

Original entry on oeis.org

3, 7, 19, 43, 67, 103, 127, 139, 199, 283, 307, 367, 379, 439, 463, 523, 547, 607, 643, 727, 739, 823, 859, 907, 1063, 1123, 1303, 1327, 1399, 1447, 1459, 1483, 1627, 1699, 1747, 1999, 2083, 2239, 2287, 2383, 2539, 2887, 3067, 3079, 3307, 3319, 3463, 3499
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 5 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 19; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(#+19)/2]&] (* Harvey P. Dale, Sep 06 2023 *)
  • PARI
    list(n)=my(t=1,p,i=1);while(i2&&bigomega((19+p)/2)==1,print(p))) \\ Anders Hellström, Jan 22 2017

A145477 Primes p such that (23 + p)/2 is prime.

Original entry on oeis.org

3, 11, 23, 59, 71, 83, 179, 191, 239, 251, 311, 359, 431, 443, 479, 491, 503, 563, 599, 683, 743, 839, 863, 911, 983, 1019, 1091, 1103, 1151, 1163, 1259, 1283, 1499, 1523, 1571, 1619, 1871, 1931, 2003, 2039, 2099, 2339, 2351, 2411, 2423, 2531, 2543, 2579
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 11 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 23; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(23+#)/2]&] (* Harvey P. Dale, Jan 26 2024 *)
  • PARI
    list(n)=my(t=1, p, i=1); while(i2&&prime((23+p)/2), print1(p, ", "))) \\ Anders Hellström, Jan 23 2017

A145478 Primes p such that (29 + p)/2 is prime.

Original entry on oeis.org

5, 17, 29, 53, 89, 113, 137, 149, 173, 197, 233, 269, 317, 353, 449, 509, 557, 593, 677, 773, 809, 857, 929, 953, 977, 1013, 1097, 1109, 1277, 1289, 1373, 1409, 1493, 1613, 1697, 1733, 1877, 1913, 1997, 2069, 2153, 2273, 2297, 2333, 2357, 2417, 2549, 2609
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 5 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 29; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
  • PARI
    first(n)=my(t=1, p, i=1); while(i2&&isprime((29+p)/2), print1(p,", "))) \\ Anders Hellström, Jan 22 2017

A145473 Primes p such that (11 + p)/2 is prime.

Original entry on oeis.org

3, 11, 23, 47, 71, 83, 107, 131, 167, 191, 251, 263, 347, 383, 443, 467, 491, 503, 683, 827, 887, 911, 947, 971, 1031, 1103, 1163, 1187, 1223, 1283, 1307, 1427, 1511, 1583, 1607, 1667, 1811, 1847, 1871, 1931, 2027, 2087, 2111, 2207, 2351, 2423, 2447, 2543
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All these primes are congruent to 3 mod 4 and (with the exception of the first term) to 11 mod 12.

Links

Crossrefs

Cf. A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 11; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[400]],PrimeQ[(#+11)/2]&] (* Harvey P. Dale, Apr 15 2012 *)
  • PARI
    first(n)=my(t=1, p, i=1); while(i2&&isprime((11+p)/2), print1(p,", "))) \\ Anders Hellström, Jan 22 2017

A145481 Primes p such that 2*p - 17 is prime.

Original entry on oeis.org

11, 17, 23, 29, 53, 59, 83, 107, 137, 149, 167, 233, 239, 263, 269, 293, 317, 347, 359, 389, 419, 449, 479, 557, 563, 599, 617, 647, 653, 659, 809, 827, 857, 863, 947, 953, 983, 1049, 1163, 1187, 1217, 1229, 1283, 1319, 1373, 1409, 1427, 1439, 1487, 1493
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

Cf. A063908-A063913, A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 17; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 250, And[PrimeQ@ #, # > 0] &[2 # - 17] &] (* Michael De Vlieger, Jan 23 2017 *)

Formula

a(n) = 2*A145475(n) - 17.

A145482 Primes p such that 2*p - 19 is prime.

Original entry on oeis.org

11, 13, 19, 31, 43, 61, 73, 79, 109, 151, 163, 193, 199, 229, 241, 271, 283, 313, 331, 373, 379, 421, 439, 463, 541, 571, 661, 673, 709, 733, 739, 751, 823, 859, 883, 1009, 1051, 1129, 1153, 1201, 1279, 1453, 1543, 1549, 1663, 1669, 1741, 1759, 1783, 1789
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

Cf. A063908-A063913, A092109, A145471-A145480.

Programs

  • Mathematica
    aa = {}; k = 19; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 300, And[PrimeQ@ #, # > 0] &[2 # - 19] &] (* Michael De Vlieger, Jan 23 2017 *)

Formula

a(n) = 2*A145476(n) - 19.
Showing 1-10 of 11 results. Next

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