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.

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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

A145479 Primes p such that (31+p)/2 is prime.

Original entry on oeis.org

3, 7, 31, 43, 103, 127, 163, 223, 271, 283, 331, 367, 523, 631, 643, 727, 787, 811, 883, 967, 1051, 1063, 1123, 1171, 1231, 1291, 1423, 1447, 1471, 1483, 1543, 1627, 1723, 1783, 1951, 1987, 2011, 2143, 2203, 2311, 2371, 2467, 2551, 2731, 2767, 2887, 3067
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Comments

All terms are congruent to 3 mod 4 and (with the exception of the first term) to 7 mod 12.

Links

Crossrefs

Cf. A092109, A145471, A145472, A145473, A145474, A145475, A145476, A145477, A145478, A145479, A155480.

Programs

  • Mathematica
    aa = {}; k = 31; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, Prime[n]]], {n, 1, 500}];aa
Select[Prime[Range[500]],PrimeQ[(31+#)/2]&] (* Harvey P. Dale, Feb 05 2012 *)
  • PARI
    list(n)=my(t=1, p, i=1); while(i2&&isprime((31+p)/2),print1(p, ", "))) \\ Anders Hellström, Jan 23 2017

A145487 Numbers k such that 6k+5 is prime and 12k+5 is also prime.

Original entry on oeis.org

0, 1, 2, 3, 4, 7, 8, 9, 11, 14, 16, 21, 22, 24, 29, 32, 37, 38, 42, 43, 46, 51, 58, 63, 64, 66, 71, 73, 77, 79, 81, 84, 92, 98, 99, 102, 106, 107, 108, 113, 119, 123, 134, 136, 142, 143, 156, 157, 158, 162, 184, 191, 196, 198, 203, 212, 217, 219, 227, 228, 238, 241, 246
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    aa = {}; k = 5; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (Prime[n] - 5)/12]], {n, 1, 500}]; aa
Select[Range[0, 250], PrimeQ[6 # + 5] && PrimeQ[12 # + 5] &] (* Ivan Neretin, Jan 21 2017 *)
Select[Range[0,250],AllTrue[5+{6#,12#},PrimeQ]&] (* Harvey P. Dale, Dec 20 2022 *)

Formula

a(n) = (A145471(n)-5)/12.

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.

A145483 Primes p such that 2*p - 23 is prime.

Original entry on oeis.org

13, 17, 23, 41, 47, 53, 101, 107, 131, 137, 167, 191, 227, 233, 251, 257, 263, 293, 311, 353, 383, 431, 443, 467, 503, 521, 557, 563, 587, 593, 641, 653, 761, 773, 797, 821, 947, 977, 1013, 1031, 1061, 1181, 1187, 1217, 1223, 1277, 1283, 1301, 1307, 1361
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    aa = {}; k = 23; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
(* Second program: *)
Select[Prime@ Range@ 240, And[PrimeQ@ #, # > 0] &[2 # - 23] &] (* Michael De Vlieger, Jan 23 2017 *)

Formula

a(n) = 2*A145477(n) - 23.

A145484 Primes p such that 2*p - 29 is a positive prime.

Original entry on oeis.org

17, 23, 29, 41, 59, 71, 83, 89, 101, 113, 131, 149, 173, 191, 239, 269, 293, 311, 353, 401, 419, 443, 479, 491, 503, 521, 563, 569, 653, 659, 701, 719, 761, 821, 863, 881, 953, 971, 1013, 1049, 1091, 1151, 1163, 1181, 1193, 1223, 1289, 1319, 1361, 1409
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    aa = {}; k = 29; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa (* Artur Jasinski *)
Select[Prime[Range[7,300]],PrimeQ[2#-29]&] (* Harvey P. Dale, Dec 14 2010 *)

Formula

a(n) = 2*A145478(n) - 29.

A145485 Primes p such that 2*p - 31 is prime.

Original entry on oeis.org

17, 19, 31, 37, 67, 79, 97, 127, 151, 157, 181, 199, 277, 331, 337, 379, 409, 421, 457, 499, 541, 547, 577, 601, 631, 661, 727, 739, 751, 757, 787, 829, 877, 907, 991, 1009, 1021, 1087, 1117, 1171, 1201, 1249, 1291, 1381, 1399, 1459, 1549, 1597, 1609, 1669
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    aa = {}; k = 31; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
  • PARI
    list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(2*p-31), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

Formula

a(n) = 2*A145479(n) - 31.

A145486 Primes p such that 2*p - 37 is prime.

Original entry on oeis.org

37, 67, 73, 97, 109, 139, 157, 193, 223, 229, 307, 349, 373, 397, 433, 457, 487, 523, 577, 619, 643, 709, 733, 823, 829, 853, 907, 919, 1033, 1063, 1087, 1129, 1153, 1213, 1237, 1279, 1297, 1327, 1447, 1543, 1549, 1579, 1609, 1627, 1669, 1699, 1747, 1753
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    aa = {}; k = 37; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (k + Prime[n])/2]], {n, 1, 500}];aa
  • PARI
    list(lim)=my(v=List()); forprime(p=2,lim, if(isprime(2*p-37), listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Jan 23 2017

Formula

a(n)=2*A145480(n)-37

A145488 Numbers k such that 6k+13 is prime and 12k+13 is also prime.

Original entry on oeis.org

0, 4, 5, 8, 14, 15, 19, 25, 28, 30, 33, 35, 44, 49, 50, 54, 60, 68, 70, 85, 88, 93, 99, 100, 103, 120, 123, 133, 140, 144, 145, 149, 154, 168, 170, 173, 175, 179, 184, 190, 198, 215, 228, 235, 245, 253, 259, 264, 268, 274, 275, 280, 285, 288, 294
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Maple
    select(k -> isprime(6*k+13) and isprime(12*k+13), [$0..1000]); # Robert Israel, Jan 23 2017
  • Mathematica
    aa = {}; k = 13; Do[If[PrimeQ[(k + Prime[n])/2], AppendTo[aa, (Prime[n] - k)/12]], {n, 1, 500}]; aa

Formula

a(n) = (A145474(n)-13)/12.

Extensions

Definition corrected by Ivan Neretin, Jan 23 2017
Previous Showing 11-20 of 22 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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