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 1-8 of 8 results.

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.

A337480 Numbers k such that exactly one of 6*k + 5 and 12*k + 5 is prime.

Original entry on oeis.org

6, 12, 13, 17, 18, 19, 23, 26, 27, 28, 31, 33, 39, 41, 44, 47, 48, 49, 52, 53, 54, 56, 57, 59, 67, 68, 69, 74, 76, 78, 83, 86, 87, 88, 91, 93, 94, 97, 101, 109, 112, 114, 116, 117, 124, 126, 128, 129, 132, 133, 137, 139, 141, 144, 146, 147, 151, 154, 159, 161
Offset: 1

Views

Author

K. D. Bajpai, Aug 28 2020

Keywords

Examples

			a(5) = 18 is a term because 6*18 + 5 = 113 is prime; but 12*18 + 5 = 221 = (13*17) is a composite number.
a(8) = 26 is a term because 6*26 + 5 = 161 = (7*23) is a composite number; but 12*26 + 5 = 317 is prime.

Links

Crossrefs

Cf. A063913, A145487, A145490, A172287.

Programs

  • Maple
    A337480:=k->`if`(isprime(6*k+5) xor isprime(12*k+5),k, NULL): seq(A337480(k), k=1..1000);
  • Mathematica
    Select[Range[0, 250], Xor[PrimeQ[6 # + 5], PrimeQ[12 # + 5]] &]
  • PARI
    for(k=1, 1000, if (bitxor(isprime(6*k+5), isprime(12*k+5)), print1(k, ", ")));

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

A145489 Numbers k such that 6k + 11 is prime and 12k + 5 is also prime.

Original entry on oeis.org

0, 1, 2, 3, 7, 8, 12, 16, 21, 23, 26, 37, 38, 42, 43, 47, 51, 56, 58, 63, 68, 73, 78, 91, 92, 98, 101, 106, 107, 108, 133, 136, 141, 142, 156, 157, 162, 173, 192, 196, 201, 203, 212, 218, 227, 233, 236, 238, 246, 247, 257, 267, 268, 271, 287, 296, 306, 313, 316, 323, 327, 332, 346, 353, 357, 366, 367, 371, 376, 387, 401, 406, 411, 423, 441, 442, 448, 453, 471, 472, 478, 483, 488, 491, 498
Offset: 1

Views

Author

Artur Jasinski, Oct 11 2008

Keywords

Links

Crossrefs

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

Programs

  • Mathematica
    Select[Range[0,500], PrimeQ[6# + 11 ] && PrimeQ[12# + 5]&]
  • PARI
    isok(n) = isprime(6*n+11) && isprime(12*n+5); \\ Michel Marcus, Jan 24 2017

Formula

a(n) = (A145475(n) - 5)/12.

Extensions

Corrected by Artur Jasinski, Apr 01 2011
Showing 1-8 of 8 results.

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

Content is available under The OEIS End-User License Agreement.